Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913129650192384 |
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| author | Kuhrman, Judson |
| author_facet | Kuhrman, Judson |
| contents | We establish a formula expressing Miyazawa's 2-knot invariant $|\mathrm{deg}|$ in terms of the Lefschetz number of a map on ordinary (i.e., not real) monopole Floer homology. As an application, we deduce that $|\mathrm{deg}|=1$ for any 2-knot in $S^4$ which has a punctured $L$-space as a Seifert solid. In the course of the proof of the main theorem, we show how Francesco Lin's construction of monopole Floer homology with $\operatorname{Pin}(2)$-equivariant perturbations can be made to work with integer coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14996 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids Kuhrman, Judson Geometric Topology 57K41 (Primary), 57K45 (Secondary) We establish a formula expressing Miyazawa's 2-knot invariant $|\mathrm{deg}|$ in terms of the Lefschetz number of a map on ordinary (i.e., not real) monopole Floer homology. As an application, we deduce that $|\mathrm{deg}|=1$ for any 2-knot in $S^4$ which has a punctured $L$-space as a Seifert solid. In the course of the proof of the main theorem, we show how Francesco Lin's construction of monopole Floer homology with $\operatorname{Pin}(2)$-equivariant perturbations can be made to work with integer coefficients. |
| title | Miyazawa's Invariant, Lefschetz Numbers, and Seifert Solids |
| topic | Geometric Topology 57K41 (Primary), 57K45 (Secondary) |
| url | https://arxiv.org/abs/2605.14996 |