Seminar in Topology and Symplectic Geometry

from Monday
January 01, 2018 to Thursday
May 31, 2018
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Thursday
February 08, 2018

1:00 PM - 2:15 PM
Math Tower 5-127
Kristen Hendricks, Michigan State University
Connected Heegaard Floer homology and homology cobordism

We study applications of Heegaard Floer homology to homology cobordism. In particular, to a homology sphere Y, we define a module HF_conn(Y), called the connected Heegaard Floer homology of Y, and show that this module is invariant under homology cobordism and isomorphic to a summand of HF_red(Y). The definition of this invariant relies on involutive Heegaard Floer homology. We use this to define a new filtration on the homology cobordism group, and to give a reproof of Furuta's theorem. This is joint work with Jen Hom and Tye Lidman.


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