Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Peano dimension of fundamental groups   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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The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom