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Pin(2)-equivariant Seiberg–Witten Floer homology of Seifert fibrations
| Content Provider | Scilit |
|---|---|
| Author | Stoffregen, Matthew |
| Copyright Year | 2019 |
| Description | Journal: Compositio Mathematica We compute the $\text{Pin}(2)$-equivariant Seiberg–Witten Floer homology of Seifert rational homology three-spheres in terms of their Heegaard Floer homology. As a result of this computation, we prove Manolescu’s conjecture that $\unicode[STIX]{x1D6FD}=-\bar{\unicode[STIX]{x1D707}}$ for Seifert integral homology three-spheres. We show that the Manolescu invariants $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD},$ and $\unicode[STIX]{x1D6FE}$ give new obstructions to homology cobordisms between Seifert fiber spaces, and that many Seifert homology spheres $\unicode[STIX]{x1D6F4}(a_{1},\ldots ,a_{n})$ are not homology cobordant to any $-\unicode[STIX]{x1D6F4}(b_{1},\ldots ,b_{n})$. We then use the same invariants to give an example of an integral homology sphere not homology cobordant to any Seifert fiber space. We also show that the $\text{Pin}(2)$-equivariant Seiberg–Witten Floer spectrum provides homology cobordism obstructions distinct from $\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD},$ and $\unicode[STIX]{x1D6FE}$. In particular, we identify an $\mathbb{F}[U]$-module called connected Seiberg–Witten Floer homology, whose isomorphism class is a homology cobordism invariant. |
| Ending Page | 250 |
| Starting Page | 199 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x19007620 |
| Journal | Compositio Mathematica |
| Issue Number | 2 |
| Volume Number | 156 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2019-12-09 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Fluids and Plasmas Physics Floer Homology Witten Floer Equivariant Seiberg |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
