A connected sum formula for involutive Heegaard Floer homology

• Kristen Hendricks ^[1] ; Ciprian Manolescu ^[2] ; Ian Zemke ^[2]
  1. [1] Michigan State University

     Michigan State University

     City of East Lansing, Estados Unidos

     
  2. [2] University of California
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 2, 2018, págs. 1183-1245
• Idioma: inglés
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• Resumen

  • 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 d––(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.