Connected Heegaard Floer homology and homology cobordism
Kristen Hendricks (Rutgers)
Location: Hill 705
Date & time: Tuesday, 03 December 2019 at 3:50PM - 4:40PM
Abstract: 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.