Ross Geoghegan, 15 mai 2008, 11h15, MA 12

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 $n\geq 0$ 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.