Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On subgroups of first homology   We prove several new theorems regarding first homology. Some dichotomies for
first homology of Peano continua are presented, as well as a notion of strong
abelianization for arbitrary path connected metric spaces. We also show that
the fundamental group of the Hawaiian earring has Borel subgroups of almost all
multiplicative and additive types.

3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: stat
6
The categories of this paper are: astro-ph