Homology three-spheres and surgery obstructions

Geometry Topology Seminar
Monday, December 1, 2014 - 2:00pm
1 hour (actually 50 minutes)
Skiles 006
University of Texas, Austin
The Lickorish-Wallace theorem states that every closed, connected, orientable three-manifold can be expressed as surgery on a link in the three-sphere (i.e., remove a neighborhood of a disjoint union of embedded $S^1$'s from $S^3$ and re-glue).  It is natural to ask which three-manifolds can be obtained by surgery on a single knot in the three-sphere.  We discuss a new way to obstruct integer homology spheres from being surgery on a knot and give some examples.  This is joint work with Jennifer Hom and Cagri Karakurt.