Joint LA Topology Seminar

Series: Caltech/USC/UCLA Joint Topology Seminar Series

Distance one lens space fillings and band surgery

Allison Moore, Department of Mathematics, UC Davis,

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.

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