Real Heegaard Floer Homology
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915652459036672 |
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| author | Guth, Gary Manolescu, Ciprian |
| author_facet | Guth, Gary Manolescu, Ciprian |
| contents | We define an invariant of three-manifolds with an involution with non-empty fixed point set of codimension $2$; 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09034 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real Heegaard Floer Homology Guth, Gary Manolescu, Ciprian Geometric Topology Symplectic Geometry 57R58, 57K18, 53D40 We define an invariant of three-manifolds with an involution with non-empty fixed point set of codimension $2$; 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. |
| title | Real Heegaard Floer Homology |
| topic | Geometric Topology Symplectic Geometry 57R58, 57K18, 53D40 |
| url | https://arxiv.org/abs/2504.09034 |