### 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 d̲(Y)≠d(Y)≠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.

Original language | English (US) |
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Pages (from-to) | 1183-1245 |

Number of pages | 63 |

Journal | Selecta Mathematica, New Series |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Apr 1 2018 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)

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## Cite this

Hendricks, K., Manolescu, C., & Zemke, I. (2018). A connected sum formula for involutive Heegaard Floer homology.

*Selecta Mathematica, New Series*,*24*(2), 1183-1245. https://doi.org/10.1007/s00029-017-0332-8