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Stable Commutator Length In Amalgamated Free Products, Timothy Susse

Dissertations, Theses, and Capstone Projects

We show that stable commutator length is rational on free products of free Abelian groups amalgamated over Z^k, 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 …