Allison Moore

Band surgery is a topological operation that transforms a knot into a new knot or link. When the operation respects orientations on the links involved, it is called coherent band surgery, otherwise it is called non-coherent. While coherent band surgery is relatively well-understood, non-coherent band surgery is less predictable. We will classify all band surgery operations from the trefoil knot to the T(2, n) torus knots and links. We accomplish this by recasting the classification problem into three-manifold topology. The three-manifold problem is solved by analyzing the behavior of the Heegaard Floer d-invariants under integral surgery along knots in the lens space L(3,1). Our interest in band surgery is motivated by DNA topology. During replication and other cellular processes, knots and links can form in circular DNA molecules. These topological problems are corrected by enzymes. In particular, the enzymatic action of site-specific recombinases is modeled by band surgery operations on knots and links. This is joint work with Lidman and Vazquez.