On the genus of infinite groups
Group Theory
2011-12-01 v1
Abstract
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.
Cite
@article{arxiv.1111.7016,
title = {On the genus of infinite groups},
author = {Iain Aitchison and Lawrence Reeves},
journal= {arXiv preprint arXiv:1111.7016},
year = {2011}
}