Framed instanton homology and Frøyshov's invariant
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912726520954880 |
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| author | Ghosh, Sudipta Eismeier, Mike Miller |
| author_facet | Ghosh, Sudipta Eismeier, Mike Miller |
| contents | We determine the framed instanton homology with coefficients in $\mathbb F = \mathbb Z/2$ for Dehn surgeries on a knot in the $3$-sphere. The dimension of these groups is seen to have a close relationship with a homology cobordism invariant due to Froyshov.
As an application, we show that $r$-surgery on a non-trivial knot cannot be nondegenerate $SU(2)$-abelian for any $|r| \le 4\lceil g(K)/2\rceil$, which is $2g(K)$ for $g$ even and $2g(K) + 2$ for $g$ odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Framed instanton homology and Frøyshov's invariant Ghosh, Sudipta Eismeier, Mike Miller Geometric Topology 57K31, 57R58 We determine the framed instanton homology with coefficients in $\mathbb F = \mathbb Z/2$ for Dehn surgeries on a knot in the $3$-sphere. The dimension of these groups is seen to have a close relationship with a homology cobordism invariant due to Froyshov. As an application, we show that $r$-surgery on a non-trivial knot cannot be nondegenerate $SU(2)$-abelian for any $|r| \le 4\lceil g(K)/2\rceil$, which is $2g(K)$ for $g$ even and $2g(K) + 2$ for $g$ odd. |
| title | Framed instanton homology and Frøyshov's invariant |
| topic | Geometric Topology 57K31, 57R58 |
| url | https://arxiv.org/abs/2511.18885 |