The equivalence between two real Seiberg-Witten Floer homologies
Geometric Topology
2026-05-27 v2
Abstract
We show that for a real rational homology sphere equipped with a real structure , the real monopole Floer homology defined by Li and the real Seiberg-Witten Floer homology defined by Konno, Miyazawa and Taniguchi are isomorphic. As corollaries, we identify some Froyshov-type invariants and prove two Smith-type inequalities.
Keywords
Cite
@article{arxiv.2510.03709,
title = {The equivalence between two real Seiberg-Witten Floer homologies},
author = {Yonghan Xiao},
journal= {arXiv preprint arXiv:2510.03709},
year = {2026}
}
Comments
v2: 52 pages, no figure. Comparing to v1, minor changes throughout and corrections in Section 2.2.4 and proof of Theorem 1.5. Accepted by Advances in Mathematics