Peano dimension of fundamental groups

Curtis Kent; Gregory Conner

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Peano dimension of fundamental groups

Gregory Conner, Curtis Kent

Algebraic Topology · Submitted 17 Feb 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove the conjecture for one-dimensional or planar Peano continua.

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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,549 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.66 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.64 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We define the Peano dimension for groups arising as fundamental groups, which generalizes the classical definition of geometric dimension of finitely presented groups. We conjecture that the Peano dimension of the fundamental group of a aspherical Peano continuum $X$ is equal to the homotopy dimension of $X$. We prove the conjecture for one-dimensional or planar Peano continua. This answers a question posed by Cannon and Conner in 2007 concerning the homotopy dimension of planar sets.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We define the Peano dimension for groups arising as fundamental groups, which generalizes the classical definition of geometric dimension of finitely presented groups.	contribution 1.00	0.94	0.07	asserted 1.00
s1	We conjecture that the Peano dimension of the fundamental group of a aspherical Peano continuum $X$ is equal to the homotopy dimension of $X$.	contribution 0.47	0.43	0.18	speculative 1.00
s2	We prove the conjecture for one-dimensional or planar Peano continua.	result 0.96	0.96	0.43	asserted 1.00
s3	This answers a question posed by Cannon and Conner in 2007 concerning the homotopy dimension of planar sets.	interpretation 0.79	0.74	0.21	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

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arXiv listing abstract v3

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full text
figures and tables
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S sections
T body sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We define the Peano dimension for groups arising as fundamental groups, which generalizes the classical definition of geometric dimension of finitely presented groups. We conjecture that the Peano dimension of the fundamental group of a aspherical Peano continuum $X$ is equal to the homotopy dimension of $X$. We prove the conjecture for one-dimensional or planar Peano continua. This answers a question posed by Cannon and Conner in 2007 concerning the homotopy dimension of planar sets.

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