New invariants of Thompson's group F

Speaker: Professor Ross Geoghegan (SUNY, Binghamton)

Time: 4:00PM

Date: Mon 26th May 2008

Location: Mathematical Sciences Seminar Room

This talk is about the Thompson group F, the group of all PL dyadic increasing homeomorphisms of the closed unit interval. This fascinating (finitely presented!) group has relevance in a number of areas of mathematics, and has been widely studied in recent years. I will describe properties of F which lead to the following Theorem: {it For each ngeq0 there is a subgroup of F of type FPn which is not of type FPn+1.} (The FP properties of a group are the ''homological finiteness properties"; FP1 is ''finitely generated", etc.) The proof involves the Bieri-Neumann-Strebel-Renz invariants of groups; these will be introduced and discussed, along with some other features of F. This is joint work with Robert Bieri and Dessislava Kochloukova.

(This talk is part of the General Interest series.)