Joint LA Topology Seminar
UCLA MS 6627
Band surgery is an operation that transforms a link into a new link. When the operation is compatible with orientations on the links involved, it is called coherent band surgery, otherwise it is called non-coherent. We will look at the behavior of the signature of a knot under non-coherent band surgery, and also classify all band surgery operations from the trefoil knot to the $T(2, n)$ torus knots and links. This classification is by way of a related three-manifold problem that we solve by studying the Heegaard Floer d-invariants under integral surgery along knots in the lens space $L(3,1)$. If time permits, I will mention some motivation for the the study of band surgery on knots from a DNA topology perspective. Parts of this project are joint work with Lidman and Vazquez.