This analysis identifies isomorphism between monopole Floer homology and Seiberg-Witten homology in rational homology spheres, suggesting further invariants.
We show that for a real rational homology sphere Y equipped with a real spinᶜ 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 Frøyshov-type invariants and prove two Smith-type inequalities.
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Yi-Xin Xiao (2025) studied this question.
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