Shelukhin's Hofer distance and a symplectic cohomology barcode for contactomorphisms
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914710129999872 |
|---|---|
| author | Cant, Dylan |
| author_facet | Cant, Dylan |
| contents | This paper constructs a persistence module of Floer cohomology groups associated to a contactomorphism of the ideal boundary of a Liouville manifold. The barcode (or, bottleneck) distance between the persistence modules is bounded from above by Shelukhin's Hofer distance. Moreover, the barcode is supported (i.e., has spectrum) on the lengths of translated points of the contactomorphism. We use this structure to prove various existence results for translated points and to construct spectral invariants for contactomorphisms which are monotone with respect to positive paths and continuous with respect to Shelukhin's Hofer distance. While this paper was nearing completion, the author was made aware of similar upcoming work by Djordjević, Uljarević, Zhang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00529 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Shelukhin's Hofer distance and a symplectic cohomology barcode for contactomorphisms Cant, Dylan Symplectic Geometry Dynamical Systems 53D40, 53D35, 55U99 This paper constructs a persistence module of Floer cohomology groups associated to a contactomorphism of the ideal boundary of a Liouville manifold. The barcode (or, bottleneck) distance between the persistence modules is bounded from above by Shelukhin's Hofer distance. Moreover, the barcode is supported (i.e., has spectrum) on the lengths of translated points of the contactomorphism. We use this structure to prove various existence results for translated points and to construct spectral invariants for contactomorphisms which are monotone with respect to positive paths and continuous with respect to Shelukhin's Hofer distance. While this paper was nearing completion, the author was made aware of similar upcoming work by Djordjević, Uljarević, Zhang. |
| title | Shelukhin's Hofer distance and a symplectic cohomology barcode for contactomorphisms |
| topic | Symplectic Geometry Dynamical Systems 53D40, 53D35, 55U99 |
| url | https://arxiv.org/abs/2309.00529 |