Geometry and Topology Seminars

Reducible Surgeries on Slice and Almost L-Space Knots

Speaker: Holt Bodish

A celebrated theorem of low dimensional topology states that any 3-manifold can be obtained from S^3 by Dehn surgery on a link. However, it is still an open question which 3-manifolds arise as Dehn surgery on a knot (a link with one component). We use tools from Heegaard Floer homology to investigate a special case of this question: when does Dehn surgery on a knot produce a reducible 3-manifold (a non-trivial connected sum of two 3-manifolds). We show that slice knots only admit reducible surgeries of a particular kind and that only certain slopes on almost L-space knots can produce reducible 3-manifolds. This is joint work with Robert DeYeso III. Read more.