Paper Citation Record · LEDGER

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one

As of 22 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2411.15943.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2411.15943 v2

Coverage vector

measured 23 of 23 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-12T13:48:56.209968Z

measured 25 of 25 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:08:07.706376Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-10T23:40:51.431077Z

Reference resolution

23 of 23 outbound references displayed

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Outbound references

Observation 6376113a-4036-46fa-89b4-ddbd48ef23c7 · 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.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one 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 1

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Observation 2009ad6c-c6a1-4daf-9221-eda61059cffd · 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.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one 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 2

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Observation 31b45d8b-7f0f-4d05-9fc7-fcef9b52f571 · outbound

This paper cites Gelbukh, Criterion for a graph to admit a good orientation in terms of l eaf blocks, Monatsh.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Gelbukh, Criterion for a graph to admit a good orientation in terms of l eaf blocks, Monatsh

Reference 3

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Observation 71ca672b-bb8e-4d57-b8fa-28ae051c8045 · 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.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one 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 4

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Observation 2d935bf5-44ec-4223-890c-c366de111095 · 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.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024

Reference 5

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Observation 81a133b1-545a-4120-b6ea-89e15a254495 · outbound

This paper cites Hempel, 3- Manifolds , AMS Chelsea Publishing, 2004.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Hempel, 3- Manifolds , AMS Chelsea Publishing, 2004

Reference 6

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Observation bb3a3706-1c95-4fde-9fec-d32bd2531f50 · outbound

This paper cites Kitazawa, On manifolds admitting fold maps with singular value sets of concentric spheres, Doctoral Dissertation, Tokyo Institute of Technology (201 4).

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Kitazawa, On manifolds admitting fold maps with singular value sets of concentric spheres, Doctoral Dissertation, Tokyo Institute of Technology (201 4)

Reference 7

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Observation 969bfc0f-0c0a-4574-934e-ad9d1d773895 · outbound

This paper cites Kitazawa, Fold maps with singular value sets of concentric spheres , Hokkaido Mathemat- ical Journal Vol.43, No.3 (2014), 327–359.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Kitazawa, Fold maps with singular value sets of concentric spheres , Hokkaido Mathemat- ical Journal Vol.43, No.3 (2014), 327–359

Reference 8

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Observation eeb2240b-1c9c-499e-b0cd-c836f8304340 · outbound

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

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Reference 9

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Observation 0c89a871-dd1d-4b00-8f78-b2101519dcff · outbound

This paper cites Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed mani- folds which may not be orientable , Methods of Functional Analysis and Topology Vol.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed mani- folds which may not be orientable , Methods of Functional Analysis and Topology Vol

Reference 10

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Observation 8c44caa0-8d7b-440f-b626-036953d4cb56 · outbound

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

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 11

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Observation c48c4dc2-4b19-4235-8758-41b95cc9e236 · outbound

This paper cites Martinez-Alfaro, I.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Martinez-Alfaro, I

Reference 12

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Observation 110e5883-ee0a-4005-8cdf-7682bb1a75b4 · outbound

This paper cites Marzantowicz and L.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Marzantowicz and L

Reference 13

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Observation 3616ca64-40ee-4d95-8f1f-603e3e4c46cf · outbound

This paper cites Masumoto and O.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Masumoto and O

Reference 14

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Observation 1d3a0235-45fd-4970-a811-52780194fd5b · outbound

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

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Realization of a graph as the Reeb graph of a Morse function on a manifold

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-12T13:48:56.188351Z

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Observation d345ff03-7ad2-4a38-8368-aced57e4f589 · outbound

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On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Unresolved cited work

Reference 16

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Observation 2f3228dd-ae81-4251-a478-230dc4247b39 · outbound

This paper cites Reeb graph invariants of Morse functions and $3$-manifold groups.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Reeb graph invariants of Morse functions and $3$-manifold groups

Reference 17

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Observation fa8b0805-4085-46fc-9f4b-f576076693be · outbound

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

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Milnor, Lectures on the h-cobordism theorem , Math

Reference 18

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Observation 97a9e3f9-6912-4118-a780-d49edcc61e84 · outbound

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On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Unresolved cited work

Reference 19

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Observation a1d504ec-345a-4e70-99d6-8dd8b1bc1a45 · outbound

This paper cites Saeki, Morse functions with sphere ﬁbers , Hiroshima Math.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Saeki, Morse functions with sphere ﬁbers , Hiroshima Math

Reference 20

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Observation 85843031-949b-424e-b2e3-952437873d83 · outbound

This paper cites an unresolved cited work.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-12T13:48:56.205117Z

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Observation 80cfdf34-68fb-4211-84f1-ce1cd07bc7c8 · outbound

This paper cites Saeki and K.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Saeki and K

Reference 22

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Observation ef1f47f7-080c-4598-a53c-dfdc8e0c1207 · 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.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T13:48:56.427034Z

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Pith citing papers

Observation eff49d91-fcfa-46f0-88d2-cdbe620dc521 · inbound

Characterizing $3$-dimensional manifolds represented as connected sums of Lens spaces, $S^2 \times S^1$, and torus bundles over the circle by certain Morse-Bott functions cites this paper.

Characterizing $3$-dimensional manifolds represented as connected sums of Lens spaces, $S^2 \times S^1$, and torus bundles over the circle by certain Morse-Bott functions On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one

Reference 11

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Observation ae1f53ca-bbac-4f7c-a287-76ece6376b58 · inbound

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles cites this paper.

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:40:51.434207Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.