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APPLICATIONS OF INVOLUTIVE HEEGAARD FLOER HOMOLOGY

Part of: Low-dimensional topology

Published online by Cambridge University Press:  04 April 2019

Kristen Hendricks ,
Jennifer Hom  and
Tye Lidman
Kristen Hendricks
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI48824, USA (hendricks@math.msu.edu)
Jennifer Hom
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA30332, USA (hom@math.gatech.edu)
Tye Lidman
Affiliation:
Department of Mathematics, North Carolina State University, Raleigh, NC27607, USA (tlid@math.ncsu.edu)
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Abstract

We use Heegaard Floer homology to define an invariant of homology cobordism. This invariant is isomorphic to a summand of the reduced Heegaard Floer homology of a rational homology sphere equipped with a spin structure and is analogous to Stoffregen’s connected Seiberg–Witten Floer homology. We use this invariant to study the structure of the homology cobordism group and, along the way, compute the involutive correction terms $\bar{d}$ and $\text{}\underline{d}$ for certain families of three-manifolds.

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 1 , January 2021 , pp. 187 - 224
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Copyright
© Cambridge University Press 2019

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Footnotes

The first author was partially supported by NSF grant DMS-1663778. The second author was partially supported by NSF grant DMS-1552285 and a Sloan Research Fellowship. The third author was partially supported by NSF grant DMS-1709702.

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