UBC Topology Seminar: Robert DeYeso

In low-dimensional topology we are often interested in determining 3-manifolds that arise as surgery along a knot, and investigating the surfaces they contain. In this talk, we study gluings X of the twisted I-bundle over the Klein bottle to knot complements, and investigate which gluings can be realized as integral Dehn surgery along a knot in S^3. All closed, orientable 3-manifolds containing a Klein bottle can be presented as such a gluing, and Heegaard Floer homology provides a way to study surgery obstructions. Using recent immersed curves techniques, we prove that if X is 8-surgery along a genus two knot and arises as such a gluing with an S^3 knot complement, then it is an L-space and the surgery knot has the same knot Floer homology as the (2,5)-torus knot.