Geometry, Topology and Dynamics Seminar
Matt Hedden
Michigan State
Irreducible homology $S^1\times S^2$s which aren't (zero) surgery on a knot
Abstract: A well-known theorem of Lickorish and Wallace states that every closed
orientable 3-manifold arises from the operation of Dehn surgery, performed
upon a link in the 3-sphere. It is interesting to ask: how many components must
such a link have? I'll survey this problem and discuss recent constructions
of manifolds with the homology of $S^1\times S^2$ which can't arise as Dehn
surgery on a knot in $S^3$. We verify this using an obstruction coming from
the Heegaard Floer homology invariants of Osváth and Szabó. Our examples
have weight one fundamental group and were constructed to answer a question
from Aschenbrenner, Friedl and Wilton's book on 3-manifold groups. This is
joint work with Thomas Mark, Kyungbae Park, and Min Hoon Kim.
Monday April 9, 2018 at 3:00 PM in SEO 636