Surgery Exact Triangles in Instanton Theory
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909353466920960 |
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| author | Bhat, Deeparaj |
| author_facet | Bhat, Deeparaj |
| contents | We prove an exact triangle relating knot instanton Floer homology to the instanton homology of surgeries along the knot. To the author's knowledge, this is the first such result in instanton homology with integer coefficients and has no analogue in Heegaard Floer homology. To illustrate the latter claim, we derive as a consequence of this triangle, building on previous computations in the literature, that the Poincaré Homology Sphere is not an instanton $L$-space with $\mathbb{Z}/2$-coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04242 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Surgery Exact Triangles in Instanton Theory Bhat, Deeparaj Geometric Topology 57R58 We prove an exact triangle relating knot instanton Floer homology to the instanton homology of surgeries along the knot. To the author's knowledge, this is the first such result in instanton homology with integer coefficients and has no analogue in Heegaard Floer homology. To illustrate the latter claim, we derive as a consequence of this triangle, building on previous computations in the literature, that the Poincaré Homology Sphere is not an instanton $L$-space with $\mathbb{Z}/2$-coefficients. |
| title | Surgery Exact Triangles in Instanton Theory |
| topic | Geometric Topology 57R58 |
| url | https://arxiv.org/abs/2311.04242 |