English

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 YY equipped with a real spinc\mathrm{spin^c} structure s\mathfrak{s}, 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