SCL and Knot Complements

Timothy Susse (CUNY Graduate Center)

Abstract: We present a topological algorithm that can be used to compute SCL in amalgams of free Abelian groups over cyclic subgroups. In particular, we will show that such groups are PQL, implying that SCL is rational for any element of the group. The most interesting examples of such groups are fundamental groups of torus knot complements. Our approach will allow us to classify and study all surfaces with boundary in these spaces and provide combinatorial proofs of some old theorems of Waldhausen.