[Binghamton Geometry/Topology Seminar] February 26

[Marco Varisco]

BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR
  http://www.math.binghamton.edu/dept/topsem/

Date:  Thursday, February 26, 2009

Time:  2:50 pm

Place:  Library North 2205
  (followed by coffee/tea in the Anderson Reading Room)

Speaker:  Ross Geoghegan

Title:  Subgroups of Thompson's group F

Abstract:  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 greater than or equal to 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 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.