Bradley Forrest
Bradley Forrest

Ph.D. (2009) Cornell University

First Position
Dissertation
Advisor:
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Abstract: The group Aut(F_{n}) of automorphisms of a finitely generated free group acts properly and cocompactly on a simplyconnected 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, simplyconnected subcomplex K, and use K to simplify a finite presentation of Aut(F_{n}) given by Armstrong, Forrest, and Vogtmann. Further, we prove that K is contained in every Aut(F_{n})invariant simplyconnected 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 J_{0} ⊂ J_{1} ⊂ J_{2} … on R_{(Σ,u)} and prove that J_{i} is idimensional and (i – 1)connected.