Dissertations, Theses, and Capstone Projects
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.
Recommended Citation
Susse, Timothy, "Stable Commutator Length in Amalgamated Free Products" (2014). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/294