Spaces over BO are thickened manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909886190714880 |
|---|---|
| author | Tanaka, Hiro Lee |
| author_facet | Tanaka, Hiro Lee |
| contents | Consider the topologically enriched category of compact smooth manifolds (possibly with corners), with morphisms given by codimension zero smooth embeddings. Now formally identify any object X with its thickening X x [-1,1]. We prove that the resulting infinity-category of thickened smooth manifolds is equivalent to the infinity-category of finite spaces over BO. (This is one formalization of the philosophy that embedding questions become homotopy-theoretic upon passage to higher dimensions.) The central tool is a geometric construction of pushouts in this infinity-category, carried out with an eye toward proving analogous results in exact symplectic geometry. Notably, the proof never invokes smooth approximation nor any h-principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09647 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spaces over BO are thickened manifolds Tanaka, Hiro Lee Algebraic Topology Geometric Topology Consider the topologically enriched category of compact smooth manifolds (possibly with corners), with morphisms given by codimension zero smooth embeddings. Now formally identify any object X with its thickening X x [-1,1]. We prove that the resulting infinity-category of thickened smooth manifolds is equivalent to the infinity-category of finite spaces over BO. (This is one formalization of the philosophy that embedding questions become homotopy-theoretic upon passage to higher dimensions.) The central tool is a geometric construction of pushouts in this infinity-category, carried out with an eye toward proving analogous results in exact symplectic geometry. Notably, the proof never invokes smooth approximation nor any h-principle. |
| title | Spaces over BO are thickened manifolds |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2307.09647 |