Correction terms of double branched covers and symmetries of immersed curves
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910673814945792 |
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| author | Hanselman, Jonathan Marengon, Marco Wong, Biji |
| author_facet | Hanselman, Jonathan Marengon, Marco Wong, Biji |
| contents | We use the immersed curves description of bordered Floer homology to study $d$-invariants of double branched covers $Σ_2(L)$ of arborescent links $L \subset S^3$. We define a new invariant $Δ_{sym}$ of bordered $\mathbb{Z}_2$-homology solid tori from an involution of the associated immersed curves and relate it to both the $d$-invariants and the Neumann-Siebenmann $\barμ$-invariants of certain fillings. We deduce that if $L$ is a 2-component arborescent link and $Σ_2(L)$ is an L-space, then the spin $d$-invariants of $Σ_2(L)$ are determined by the signatures of $L$. By a separate argument, we show that the same relationship holds when $L$ is a 2-component link that admits a certain symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02857 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Correction terms of double branched covers and symmetries of immersed curves Hanselman, Jonathan Marengon, Marco Wong, Biji Geometric Topology 57M12, 57M25, 57R58 We use the immersed curves description of bordered Floer homology to study $d$-invariants of double branched covers $Σ_2(L)$ of arborescent links $L \subset S^3$. We define a new invariant $Δ_{sym}$ of bordered $\mathbb{Z}_2$-homology solid tori from an involution of the associated immersed curves and relate it to both the $d$-invariants and the Neumann-Siebenmann $\barμ$-invariants of certain fillings. We deduce that if $L$ is a 2-component arborescent link and $Σ_2(L)$ is an L-space, then the spin $d$-invariants of $Σ_2(L)$ are determined by the signatures of $L$. By a separate argument, we show that the same relationship holds when $L$ is a 2-component link that admits a certain symmetry. |
| title | Correction terms of double branched covers and symmetries of immersed curves |
| topic | Geometric Topology 57M12, 57M25, 57R58 |
| url | https://arxiv.org/abs/2408.02857 |