Real Heegaard Floer Homology
Geometric Topology
2025-12-05 v2 Symplectic Geometry
Abstract
We define an invariant of three-manifolds with an involution with non-empty fixed point set of codimension ; in particular, this applies to double branched covers over knots. Our construction gives the Heegaard Floer analogue of Li's real monopole Floer homology. It is a special case of a real version of Lagrangian Floer homology, which may be of independent interest to symplectic geometers. The Euler characteristic of the real Heegaard Floer homology is the analogue of Miyazawa's invariant, and can be computed combinatorially for all knots.
Keywords
Cite
@article{arxiv.2504.09034,
title = {Real Heegaard Floer Homology},
author = {Gary Guth and Ciprian Manolescu},
journal= {arXiv preprint arXiv:2504.09034},
year = {2025}
}
Comments
44 pages, 14 figures. Minor corrections made in Sections 3 and 7