Topology & Geometric Group Theory Seminar

Spring 2009

1:30 – 2:30, Malott 207

Tuesday, February 24

Ross Geoghegan, Binghamton University

Subgroups of Thompson's group F

Thompson's group F is 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 briefly introduce F and describe some of its known properties. Then I will discuss the following Theorem: For each n≥0 there is a subgroup of F of type Fn which is not of type Fn+1. (The properties "type Fn" are the topological finiteness properties of groups: a group has type F1 if it is finitely generated, has type F2 if it is finitely presented, etc.)

The proof involves the Bieri-Neumann-Strebel-Renz invariants of groups; we have determined these for F, and have have proved a general product formula for these invariants. I will explain how the combination of these two ideas yields the desired subgroups of F. This is joint work with Robert Bieri and Dessislava Kochloukova.

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