Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the genus of infinite groups   We associate to each finite presentation of a group G a compact CW-complex
that is a 3-manifold in the complement of a point, and whose fundamental group
is isomorphic to G. We use this complex to define a notion of genus for G and
give examples, and also define a notion of `closed group'. A group has genus 0
if and only if it is the fundamental group of a compact orientable 3-manifold.

12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th