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.

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