## 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 F*_{n} which is not of type
F_{n+1}. (The properties "type F_{n}" are the
topological finiteness properties of groups: a group has type
F_{1} if it is finitely generated, has type F_{2} 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.

Back to seminar home page.