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)|
|Number of pages||63|
|Journal||Selecta Mathematica, New Series|
|State||Published - Apr 1 2018|
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)