Correction terms of double branched covers and symmetries of immersed curves
| Autor: | Hanselman, Jonathan, Marengon, Marco, Wong, Biji |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We use the immersed curves description of bordered Floer homology to study $d$-invariants of double branched covers $\Sigma_2(L)$ of arborescent links $L \subset S^3$. We define a new invariant $\Delta_{sym}$ 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 $\bar\mu$-invariants of certain fillings. We deduce that if $L$ is a 2-component arborescent link and $\Sigma_2(L)$ is an L-space, then the spin $d$-invariants of $\Sigma_2(L)$ 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. Comment: 61 pages, 22 figures, 2 tables. Comments welcome |
| Databáze: | arXiv |
| Externí odkaz: |
|