Naturality in real Heegaard Floer theory

Abstract

In a previous paper we defined real Heegaard Floer homology, an invariant of three-manifolds equipped with involutions. Here we prove that real Heegaard Floer homology is natural, and that it admits an action of the equivariant mapping class group. We also establish naturality of real link Floer homology and real sutured Floer homology, and give a definition of involutive real Heegaard Floer homology.

Disclosure

“the following. Theorem 4. Let (Y, τ ) be a real three-manifold and s a self-conjugate real Spinc structure. For ◦ ∈ {−, ∞, +, ˆ}, the isomorphism class of HFRI ◦ (Y, τ, s) is an invariant of the triple (Y, τ, s). Note on AI use. We used Gemini Deep Think and Claude to produce first drafts of the proofs of Propositions 3.8 and 4.22, Corollary 4.23, Lemmas 5.10, 5.11 and 5.12. The proofs were checked and then rewritten by the authors. During the revision process we used GPT-5.6”

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Classification

Drafting a complete proof for author revision

Multiplier

9

Verified

2026-08-23T19:16:02.286006Z

Structural counts