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Naturality and functoriality in involutive Heegaard Floer homology

  • Kristen Hendricks

    Rutgers University New Brunswick, New Brunswick, USA

  • Jennifer Hom

    Georgia Institute of Technology, Atlanta, USA

  • Matthew Stoffregen

    Michigan State University, East Lansing, USA

  • Ian Zemke

    Princeton University, Princeton, USA
Naturality and functoriality in involutive Heegaard Floer homology cover

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Abstract

We prove first-order naturality of involutive Heegaard Floer homology, and furthermore, construct well-defined maps on involutive Heegaard Floer homology associated to cobordisms between three-manifolds. We also prove analogous naturality and functoriality results for involutive Floer theory for knots and links. The proof relies on the doubling model for the involution, as well as several variations.

Cite this article

Kristen Hendricks, Jennifer Hom, Matthew Stoffregen, Ian Zemke, Naturality and functoriality in involutive Heegaard Floer homology. Quantum Topol. (2024), published online first

DOI 10.4171/QT/210