Naturality and functoriality in involutive  Heegaard Floer homology

Kristen Hendricks; Jennifer Hom; Matthew Stoffregen; Ian Zemke

doi:10.4171/qt/210

JournalsqtVol. 17, No. 1pp. 45–188

Naturality and functoriality in involutive Heegaard Floer homology

Kristen Hendricks
Rutgers University New Brunswick, USA
Jennifer Hom
Georgia Institute of Technology, Atlanta, USA
Matthew Stoffregen
Michigan State University, East Lansing, USA
Ian Zemke
Princeton University, USA

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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. 17 (2026), no. 1, pp. 45–188

DOI 10.4171/QT/210