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A connected sum formula for involutive Heegaard Floer homology

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Abstract

We prove a connected sum formula for involutive Heegaard Floer homology, and use it to study the involutive correction terms of connected sums. In particular, we give an example of a three-manifold with \(\underline{d}(Y) \ne d(Y) \ne \bar{d}(Y)\). We also construct a homomorphism from the three-dimensional homology cobordism group to an algebraically defined Abelian group, consisting of certain complexes (equipped with a homotopy involution) modulo a notion of local equivalence.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Kristen Hendricks

  2. Department of Mathematics, University of California, Los Angeles, CA, 90095, USA

    Ciprian Manolescu & Ian Zemke

Authors
  1. Kristen Hendricks
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  2. Ciprian Manolescu
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  3. Ian Zemke
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Corresponding author

Correspondence to Ciprian Manolescu.

Additional information

KH was partially supported by NSF Grant DMS-1506358. CM and IZ were partially supported by NSF Grant DMS-1402914.

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Hendricks, K., Manolescu, C. & Zemke, I. A connected sum formula for involutive Heegaard Floer homology. Sel. Math. New Ser. 24, 1183–1245 (2018). https://doi.org/10.1007/s00029-017-0332-8

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