Year: 2026
Type: preprint
Abstract: Fix a 3-manifold $Y$ with boundary $F\amalg F$ and an orientation-preserving involution $τ: Y\to Y$ exchanging the boundary components, with nonempty fixed set. To an appropriate kind of Heegaard diagram for $Y$, we describe how to associate a module over the bordered Heegaard Floer algebra of $F$. These modules satisfy a gluing, or pairing, theorem, and extend the "hat" variant of Guth-Manolescu's real Heegaard Floer homology, $\widehat{HFR}(Y,τ)$. Using these modules, we give a practical algorithm to compute $\widehat{HFR}(Y,τ)$ for real 3-manifolds $(Y,τ)$ with connected fixed set.
Source: arXiv (Cornell University)
Authors: Lipshitz, Robert, Ozsváth, Peter
Institutions: University of Oregon, Princeton University
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7155397282
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