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Topology/Geometry Seminar

A zero surgery obstruction from involutive Heegaard Floer homology

Peter Johnson (University of Virginia)

Location:  zoom
Date & time: Tuesday, 28 September 2021 at 11:00AM - 12:00PM

Abstract: A fundamental result in 3-manifold topology due to Lickorish and Wallace says that every closed oriented connected 3-manifold can be realized as surgery on a link in the 3-sphere. One may therefore ask: which 3-manifolds can be obtained by surgery on a link with a single component, i.e. a knot, in the 3-sphere? More specifically, one can ask: which 3-manifolds are obtained by zero surgery on a knot in the 3-sphere? In this talk, we give a brief outline of some known results to this question in the context of small Seifert fibered spaces. We then sketch a new method, using involutive Heegaard Floer homology, to show that certain 3-manifolds cannot be obtained by zero surgery on a knot in the three sphere. In particular, we produce a new infinite family of weight 1 irreducible small Seifert fibered spaces with first homology Z which cannot be obtained by zero surgery on a knot in the 3-sphere, extending a result of Hedden, Kim, Mark and Park.