Professor Ross Geoghegan (SUNY, Binghamton)

will speak on

New invariants of Thompson's group $F$

Time: 4:00PM
Date: Mon 26th May 2008
Location: Mathematical Sciences Seminar Room [map]

Abstract: 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 $ngeq 0$ there is a subgroup of $F$ of type $FP_n$ which is not of type $FP_{n+1}$.} (The $FP$ properties of a group are the ``homological finiteness properties"; $FP_1$ 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.)

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