Framed instanton homology of surgeries on L-space knots
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866910591519555584 |
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| author | Lidman, Tye Pinzon-Caicedo, Juanita Scaduto, Christopher |
| author_facet | Lidman, Tye Pinzon-Caicedo, Juanita Scaduto, Christopher |
| contents | An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framed instanton Floer homology of all integral surgeries. As a consequence, if a knot has a Heegaard Floer and instanton Floer L-space surgery, then the theories agree for all integral surgeries. In order to prove the main result, we prove that the Baldwin-Sivek contact invariant in framed instanton Floer homology is homogeneous with respect to the absolute $\mathbb{Z}/2$-grading, but not the $\mathbb{Z}/4$-grading. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_03329 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Framed instanton homology of surgeries on L-space knots Lidman, Tye Pinzon-Caicedo, Juanita Scaduto, Christopher Geometric Topology 57K31, 57K33, 57R58 An important class of three-manifolds are L-spaces, which are rational homology spheres with the smallest possible Floer homology. For knots with an instanton L-space surgery, we compute the framed instanton Floer homology of all integral surgeries. As a consequence, if a knot has a Heegaard Floer and instanton Floer L-space surgery, then the theories agree for all integral surgeries. In order to prove the main result, we prove that the Baldwin-Sivek contact invariant in framed instanton Floer homology is homogeneous with respect to the absolute $\mathbb{Z}/2$-grading, but not the $\mathbb{Z}/4$-grading. |
| title | Framed instanton homology of surgeries on L-space knots |
| topic | Geometric Topology 57K31, 57K33, 57R58 |
| url | https://arxiv.org/abs/2003.03329 |