A knot Floer stable homotopy type
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909779419463680 |
|---|---|
| author | Manolescu, Ciprian Sarkar, Sucharit |
| author_facet | Manolescu, Ciprian Sarkar, Sucharit |
| contents | Given a grid diagram for a knot or link K in $S^3$, we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13566 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A knot Floer stable homotopy type Manolescu, Ciprian Sarkar, Sucharit Geometric Topology Algebraic Topology Symplectic Geometry 57K18 Given a grid diagram for a knot or link K in $S^3$, we construct a filtered spectrum whose homology is the knot Floer homology of K. We conjecture that the filtered homotopy type of the spectrum is an invariant of K. Our construction does not use holomorphic geometry, but rather builds on the combinatorial definition of grid homology. We inductively define models for the moduli spaces of pseudo-holomorphic strips and disk bubbles, and patch them together into a framed flow category. The inductive step relies on the vanishing of an obstruction class that takes values in a complex of positive domains with partitions. |
| title | A knot Floer stable homotopy type |
| topic | Geometric Topology Algebraic Topology Symplectic Geometry 57K18 |
| url | https://arxiv.org/abs/2108.13566 |