Naturality and functoriality in involutive Heegaard Floer homology

Kristen Hendricks; Jennifer Hom; Matthew Stoffregen; Ian Zemke

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arXiv · 2201.12906

Naturality and functoriality in involutive Heegaard Floer homology

Kristen Hendricks·Jennifer Hom·Matthew Stoffregen·Ian Zemke

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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.

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Kristen Hendricks, Jennifer Hom, Matthew Stoffregen, Ian Zemke. 2022-01-30. Naturality and functoriality in involutive Heegaard Floer homology. https://arxiv.org/abs/2201.12906

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