Bradley Forrest

Bradley Forrest
Ph.D. (2009) Cornell University

First Position

Assistant professor at the Richard Stockton College of New Jersey

Dissertation

Degree Subcomplexes of Auter Space and Ribbon Graph Complexes

Advisor:


Research Area:
Topology and geometric group theory

Abstract: The group Aut(Fn) of automorphisms of a finitely generated free group acts properly and cocompactly on a simply-connected simplicial complex known as the degree 2 subcomplex of the spine of Auter space. In the first part of this thesis, we show that the degree 2 subcomplex contains a proper, invariant, simply-connected subcomplex K, and use K to simplify a finite presentation of Aut(Fn) given by Armstrong, Forrest, and Vogtmann. Further, we prove that K is contained in every Aut(Fn)-invariant simply-connected subcomplex of the degree 2 subcomplex.

The mapping class group of an orientable, basepointed, punctured surface (Σ,u) acts properly and cocompactly on a simplicial complex known as R(Σ,u) the ribbon graph complex of (Σ,u). We define a filtration J0 ⊂ J1 ⊂ J2 … on R(Σ,u) and prove that Ji is i-dimensional and (i – 1)-connected.