Skein relations for tangle Floer homology
| Autor: | C.-M. Michael Wong, Ina Petkova |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Skein
Skein relation Geometric Topology (math.GT) Mathematics::Algebraic Topology Mathematics::Geometric Topology Tangle Combinatorics Mathematics - Geometric Topology Floer homology Mathematics::K-Theory and Homology Mathematics::Quantum Algebra FOS: Mathematics Bimodule Geometry and Topology Mathematics::Symplectic Geometry Mathematical Physics Differential (mathematics) Mathematics Knot (mathematics) |
| Zdroj: | Quantum Topology. 11:119-225 |
| ISSN: | 1663-487X |
| Popis: | In a previous paper, V\'ertesi and the first author used grid-like Heegaard diagrams to define tangle Floer homology, which associates to a tangle $T$ a differential graded bimodule $\widetilde{\mathrm{CT}} (T)$. If $L$ is obtained by gluing together $T_1, \dotsc, T_m$, then the knot Floer homology $\hat{\mathrm{HFK}}(L)$ of $L$ can be recovered from $\widetilde{\mathrm{CT}} (T_1), \dotsc, \widetilde{\mathrm{CT}} (T_m)$. In the present paper, we prove combinatorially that tangle Floer homology satisfies unoriented and oriented skein relations, generalizing the skein exact triangles for knot Floer homology. Comment: 72 pages, 48 figures, 5 tables. Minor revisions |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|