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Morse theory and finiteness properties of groups
by
Mladen Bestvina
University of Utah
Coauthors: Noel Brady
A hierarchy of finiteness properties of groups was introduced by C.T.C. Wall. A group has type Fn if it acts freely and cocompactly on an (n-1)-connected CW-complex. For example, F1 means ``finitely generated'' and F2 means ``finitely presented''. There is also the corresponding homological notion, where one replaces ``(n-1)-connected'' by ``(n-1)-acyclic''. In this talk I will discuss how one can detect such properties in groups using Morse theory. In particular, I will show an example of a group that acts freely and cocompactly on a 2-dimensional acyclic complex but fails to be finitely presented. This is a joint work with Noel Brady.
Date received: February 11, 1998
Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caas-54.