Lattice homology, formality, and plumbed L-space links
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914703700131840 |
|---|---|
| author | Borodzik, Maciej Liu, Beibei Zemke, Ian |
| author_facet | Borodzik, Maciej Liu, Beibei Zemke, Ian |
| contents | We define a link lattice complex for plumbed links, generalizing constructions of Ozsváth, Stipsicz and Szabó, and of Gorsky and Némethi. We prove that for all plumbed links in rational homology 3-spheres, the link lattice complex is homotopy equivalent to the link Floer complex as an $A_\infty$-module. Additionally, we prove that the link Floer complex of a plumbed L-space link is a free resolution of its homology. As a consequence, we give an algorithm to compute the link Floer complexes of plumbed L-space links, in particular of algebraic links, from their multivariable Alexander polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_15792 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Lattice homology, formality, and plumbed L-space links Borodzik, Maciej Liu, Beibei Zemke, Ian Geometric Topology Algebraic Geometry 57K10, 57K18, 57R58, 14B05, 14J17, 14H20 We define a link lattice complex for plumbed links, generalizing constructions of Ozsváth, Stipsicz and Szabó, and of Gorsky and Némethi. We prove that for all plumbed links in rational homology 3-spheres, the link lattice complex is homotopy equivalent to the link Floer complex as an $A_\infty$-module. Additionally, we prove that the link Floer complex of a plumbed L-space link is a free resolution of its homology. As a consequence, we give an algorithm to compute the link Floer complexes of plumbed L-space links, in particular of algebraic links, from their multivariable Alexander polynomial. |
| title | Lattice homology, formality, and plumbed L-space links |
| topic | Geometric Topology Algebraic Geometry 57K10, 57K18, 57R58, 14B05, 14J17, 14H20 |
| url | https://arxiv.org/abs/2210.15792 |