Selecta Mathematica

, Volume 24, Issue 2, pp 1183–1245 | Cite as

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.

Mathematics Subject Classification

57R58 (Primary) 57M27 (Secondary) 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  • Kristen Hendricks
    • 1
  • Ciprian Manolescu
    • 2
  • Ian Zemke
    • 2
  1. 1.Department of MathematicsMichigan State UniversityEast LansingUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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