Mathematical Research Letters
Volume 19 (2012)
On the genus of infinite groups
Pages: 601 – 612
We associate to each finite presentation of a group $G$ acompact CW-complex that is a 3-manifold in the complementof 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 ‘closedgroup’. A group has genus 0 if and only if it is thefundamental group of a compact orientable 3-manifold.
geometric group theory, genus
2010 Mathematics Subject Classification