On the genus of infinite groups

Details On the genus of infinite groups On the genus of infinite groups

2011-11-29

arxiv.org/abs/1111.7016v1

Mathematics

Group Theory

Scientific paper

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.

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