Date of Degree

6-2014

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Jason Behrstock

Subject Categories

Mathematics

Keywords

Geometric Group Theory, Group Theory, Stable Commutator Length, Surfaces, Topology

Abstract

We show that stable commutator length is rational on free products of free Abelian groups amalgamated over Zk, a class of groups containing the fundamental groups of all torus knot complements. We consider a geometric model for these groups and parameterize all surfaces with specified boundary mapping to this space. Using this work we provide a topological algorithm to compute stable commutator length in these groups. We then use the combinatorics of this algorithm to prove that for a word w in the (p, q)-torus knot complement, scl(w) is quasirational in p and q. Finally, we analyze central extensions, and prove that under certain conditions the projection map preserves stable commutator length.

Included in

Mathematics Commons

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