The equivalence between two real Seiberg-Witten Floer homologies
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916048124510208 |
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| author | Xiao, Yonghan |
| author_facet | Xiao, Yonghan |
| contents | We show that for a real rational homology sphere $Y$ equipped with a real $\mathrm{spin^c}$ structure $\mathfrak{s}$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03709 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The equivalence between two real Seiberg-Witten Floer homologies Xiao, Yonghan Geometric Topology 57R58, 57R57 We show that for a real rational homology sphere $Y$ equipped with a real $\mathrm{spin^c}$ structure $\mathfrak{s}$, 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. |
| title | The equivalence between two real Seiberg-Witten Floer homologies |
| topic | Geometric Topology 57R58, 57R57 |
| url | https://arxiv.org/abs/2510.03709 |