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Paper Citation Record · LEDGER

Fundamental examples of height functions on closed manifolds and their 1st derivatives

As of 13 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2608.00556.

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pith.paper-citation-record.v1
2608.00556 v1

Coverage vector

measured 49 of 49 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-05T00:54:17.047306Z

measured 49 of 49 standing notices

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Reference resolution

49 of 49 outbound references displayed

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Outbound references

Observation e8584070-7ed4-4784-9972-5c83fedde0f0 · outbound

This paper cites Banyaga and D.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Banyaga and D

Reference 1

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Observation 5d3a06ec-39cf-4590-8f7a-c81786a61041 · outbound

This paper cites Banchoff and F.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Banchoff and F

Reference 2

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Observation 0147e878-477c-4ca4-83a2-760e1a53c07f · outbound

This paper cites Burlet and V.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Burlet and V

Reference 3

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Observation b79e3abb-cee9-4bb6-82c2-a7293056e89f · outbound

This paper cites Bott, Nondegenerate critical manifolds , Ann.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Bott, Nondegenerate critical manifolds , Ann

Reference 4

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Observation ca835993-5969-4a38-bcd9-993e9490208e · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

Reference 5

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Observation 5e19cef3-8121-484c-b883-06f674dc27e7 · outbound

This paper cites Burlet and G.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Burlet and G

Reference 6

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Observation 89778b40-be1f-4efd-b6c9-a32ce320eaa7 · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

Reference 7

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Observation 43fbbb40-07ea-42d4-8b33-2ff92042d557 · outbound

This paper cites Gelbukh, A finite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, A finite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018

Reference 8

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Observation a4ed3d6c-44ce-487f-87f4-ac9242d20a1a · outbound

This paper cites Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ

Reference 9

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Observation 963b031d-7408-44aa-8790-ad88b791b275 · outbound

This paper cites Gelbukh, Realization of a graph as the Reeb graph of a height function o n an embedded surface, Topol.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Realization of a graph as the Reeb graph of a height function o n an embedded surface, Topol

Reference 10

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Observation 69a85b87-1620-4d8b-95af-2a6d4a6d1e7d · outbound

This paper cites Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–

Reference 11

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Observation e2251e1b-0f81-4bbb-a04a-e2db61f16658 · outbound

This paper cites Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024

Reference 12

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Observation 563387ff-6070-4d5f-bbd6-479d755ea6ea · outbound

This paper cites Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17

Reference 13

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Observation 8d55b1e2-28f1-4454-b316-612ab3fcf19f · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

Reference 14

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Observation 82605845-16aa-4db4-89b9-d5527f3f0c37 · outbound

This paper cites Golubitsky and V.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Golubitsky and V

Reference 15

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Observation a5c30dc0-a66d-4ab1-af7f-2777d73f0177 · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

Reference 16

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Observation 25dea9b2-7d08-407b-baa3-58ab36094df2 · outbound

This paper cites On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values.

Fundamental examples of height functions on closed manifolds and their 1st derivatives On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Reference 17

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Observation d4a3b6e0-0d81-40bf-ae2f-ad35a2329ec2 · outbound

This paper cites On Reeb graphs induced from smooth functions on closed or open manifolds.

Fundamental examples of height functions on closed manifolds and their 1st derivatives On Reeb graphs induced from smooth functions on closed or open manifolds

Reference 18

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Observation 0f8ead0f-b7bb-4df8-a540-ae1b4d4afbb4 · outbound

This paper cites Real algebraic functions on closed manifolds whose Reeb spaces are given graphs.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Real algebraic functions on closed manifolds whose Reeb spaces are given graphs

Reference 19

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Observation e167c158-d63a-4da3-8877-28e5efa14e5a · outbound

This paper cites Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 20

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This paper cites Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space

Reference 21

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This paper cites Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres

Reference 22

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Observation 64fb4e93-a10e-4c0f-bd7e-bcd2450267a4 · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation 3fb814f6-cb3f-411c-9291-d460e7c39494 · outbound

This paper cites Kitazawa, Fundamental examples of Reeb spaces of smooth functions defi ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Kitazawa, Fundamental examples of Reeb spaces of smooth functions defi ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2

Reference 24

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Observation c3ca4fb5-96b6-464e-9652-3f411e29625f · outbound

This paper cites Regions represented as foliated forms and natural smooth maps onto them.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Regions represented as foliated forms and natural smooth maps onto them

Reference 25

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Observation c14033b5-e6dd-4074-8dae-9c2f6d178c22 · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation 202d5e83-e071-4a28-a670-28eab3a446c7 · outbound

This paper cites Martinez-Alfaro, I.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Martinez-Alfaro, I

Reference 27

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Observation 37ef1885-c803-462a-b8d5-fc5faf56922e · outbound

This paper cites Masumoto and O.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Masumoto and O

Reference 28

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Observation c4253306-5c6d-43ad-810d-8e85c3b41d59 · outbound

This paper cites N Mather, Stability of C∞ mappings.

Fundamental examples of height functions on closed manifolds and their 1st derivatives N Mather, Stability of C∞ mappings

Reference 29

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Observation 9b511d86-c346-4bfd-98de-684683188e4c · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation 1a3a6a9d-2ef2-435a-891d-50826283d9ab · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation 24a45bc1-332f-49cb-9df1-bf4c023b5965 · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation 1c2b0c48-01f8-4a69-a000-a0cf0b780c29 · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation 29433566-c28b-4599-ae78-c712cbb5070a · outbound

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Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

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Observation f6080977-5c33-4fe4-b0a8-b3495cc054c6 · outbound

This paper cites Mather, Notes on topological stability , Bull.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Mather, Notes on topological stability , Bull

Reference 36

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source=pdf_text observed=2026-08-05T00:54:17.009122Z digest=sha256:77759f9dbd8d16de1f71224abb1e74f814a5275a650baac3d1240b939f000fb2

Observation 719236fb-8068-4ec7-86be-65597ec51c18 · outbound

This paper cites Realization of a graph as the Reeb graph of a Morse function on a manifold.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Realization of a graph as the Reeb graph of a Morse function on a manifold

Reference 37

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Source-reported events for the cited work

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source=pdf_text observed=2026-08-05T00:54:17.011798Z digest=sha256:85a47e8e12727d535666c2975dd5b7b2489ca61629d1929f32dfdff315ccf44f

Observation da1fbe2a-7b74-420f-a84d-400b9e309c74 · outbound

This paper cites Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1).

Fundamental examples of height functions on closed manifolds and their 1st derivatives Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1)

Reference 38

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no resolver link, observed 2026-08-05T00:54:17.014734Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.014734Z digest=sha256:622918dcc5b21c46c26d250b7a86b6359b3db1aa273b075474b54ab02efe9a25

Observation 8f2c1365-65b5-4431-b5fc-74e069db44c5 · outbound

This paper cites Milnor, Lectures on the h-cobordism theorem , Math.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Milnor, Lectures on the h-cobordism theorem , Math

Reference 39

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verified fuzzy
raw_fallback, observed 2026-08-05T00:54:17.672063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T00:54:17.017497Z digest=sha256:8fc781b8f5b78f66b3393f53f811aeb24c22589fa49d12f48c1511f2714d3638

Observation c8932ef7-b193-4fee-8297-12fefe3896aa · outbound

This paper cites Morishita and O.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Morishita and O

Reference 40

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raw_fallback, observed 2026-08-05T00:54:17.662043Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T00:54:17.020272Z digest=sha256:a193f207eb4c206c0588a47fbef8ffb909459106f4f35d96aa06bc800aefbd08

Observation 5fc54445-424e-491d-b92e-fe8431715269 · outbound

This paper cites an unresolved cited work.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

Reference 41

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no resolver link, observed 2026-08-05T00:54:17.023546Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.023546Z digest=sha256:8310b3113c5934b27c25f70f97c5451ddf313b39ff03f2d08c8f4e3dc4906f7b

Observation 4e420f73-c8ba-47b4-8b0a-e2c9aa22c61b · outbound

This paper cites Saeki, Notes on the topology of folds , J.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Notes on the topology of folds , J

Reference 42

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no resolver link, observed 2026-08-05T00:54:17.026457Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.026457Z digest=sha256:9ab44c64f088643f354dd9ad793c9f7dd78c59bb796c3eedfdeeb35fcf0b4d32

Observation 52c98521-acc9-4762-ad0f-c948e8543e3b · outbound

This paper cites Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl

Reference 43

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no resolver link, observed 2026-08-05T00:54:17.029470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.029470Z digest=sha256:b7483aca45bba3cba588ea79ee87ef8bf3f62f8b538e235eae2799e33b82bdfa

Observation c9482f1b-ed65-4c49-848b-5146fcad1bb3 · outbound

This paper cites Saeki, Topology of singular fibers of differentiable maps , Lecture Notes in Math., Vol.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Topology of singular fibers of differentiable maps , Lecture Notes in Math., Vol

Reference 44

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no resolver link, observed 2026-08-05T00:54:17.032535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.032535Z digest=sha256:37c34dc28b64f27443c451742e7539e1e79611964df8eec1ba047de8fefd12da

Observation b8a750d7-7be9-41b8-b7fc-4df79261a713 · outbound

This paper cites an unresolved cited work.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work

Reference 45

Resolution
verified exact
raw_fallback, observed 2026-08-05T00:54:17.176363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-05T00:54:17.035269Z digest=sha256:736f51415ae663beae4624ec0dc5af2dcfb40aef310da9cddd7d74cb8ae8e526

Observation a7c7dd44-499a-441e-9014-8c9191a96e44 · outbound

This paper cites Saeki, Reeb spaces of smooth functions on manifolds II , Res.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Reeb spaces of smooth functions on manifolds II , Res

Reference 46

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no resolver link, observed 2026-08-05T00:54:17.038102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.038102Z digest=sha256:f57bfe86ddf581c377a7d1509271307d51215b9f8d667d2ed28a85289a5feb22

Observation 9fbb6d04-a343-413d-b967-69b9c20dd7eb · outbound

This paper cites Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396

Reference 47

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no resolver link, observed 2026-08-05T00:54:17.041081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.041081Z digest=sha256:0ebbe1bc31f5d6cc42113fb8021dd43422fe4c579f10cf22335ef66926565a4f

Observation 27f67d91-8329-41aa-b1e3-13ad555b6f8e · outbound

This paper cites Thom, Les singularites des applications differentiables , Ann.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Thom, Les singularites des applications differentiables , Ann

Reference 48

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no resolver link, observed 2026-08-05T00:54:17.044071Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:17.044071Z digest=sha256:609b28cf956cdfedea0247fd7df68aba86155dcd29eba0c75dca411a8d0cf6e9

Observation 1ad9c0c5-39f0-49a3-8baf-5546be47fc18 · outbound

This paper cites Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann.

Fundamental examples of height functions on closed manifolds and their 1st derivatives Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann

Reference 49

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source=pdf_text observed=2026-08-05T00:54:17.047306Z digest=sha256:de2a0b89fe9bbd43d35b235e723c98c1ba67adcb1223bec9dd5182db896806ed

Pith citing papers

No inbound Pith citation observations are available.