## Topology & Geometric Group Theory Seminar

## Fall 2010

### 1:30 – 2:30, Malott 253

Tuesday, September 14

** Justin
Moore**, Cornell University

*The Laver tables and Thompson's group F*

It remains open whether Thompson's group *F* is amenable.
Recently I have demonstrated that both (a) any Følner function
for *F* must grow faster than any finite iterate of the
exponential function and (b) that Følner sequences
for *F* must exhibit certain non trivial qualitative
properties. Both suggest that Følner sets for *F*, if
they exist, should be constructed in a recursive manner and point to
features that this recursive construction should have.

The purpose of this talk is to describe a novel approach to
constructing such (potential) Følner sets. The construction is
based around factorization in certain finite algebraic structures
known as Laver tables. These algebraic structures are characterized
as being finite, monogenic, and left self distributive. The talk will
give an introduction to these tables and their properties (which are
of interest in their own right). It will finish by detailing some
properties of the Laver tables whose only known proofs require large
cardinal axioms (which are not provable in ZFC) and a conjecture
concerning the relationship of these properties to the amenability
of *F*.

Back to seminar home page.