Vector bundle automorphisms preserving Morse-Bott foliations
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_ | 1866910602957422592 |
|---|---|
| author | Maksymenko, Sergiy |
| author_facet | Maksymenko, Sergiy |
| contents | Let $M$ be a smooth manifold and $\mathcal{F}$ a Morse-Bott foliation on $M$ with a compact critical manifold $Σ$. Denote by $\mathcal{D}(\mathcal{F})$ the group of diffeomorphisms of $M$ leaving invariant each leaf of $\mathcal{F}$. Under certain assumptions on $\mathcal{F}$ it is shown that the computation of the homotopy type of $\mathcal{D}(\mathcal{F})$ reduces to three rather independent groups: the group of diffeomorphisms of $Σ$, the group of vector bundle automorphisms of some regular neighborhood of $Σ$, and the subgroup of $\mathcal{D}(\mathcal{F})$ consisting of diffeomorphisms fixed near $Σ$. Examples of computations of homotopy types of groups $\mathcal{D}(\mathcal{F})$ for such foliations are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13176 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Vector bundle automorphisms preserving Morse-Bott foliations Maksymenko, Sergiy Geometric Topology Algebraic Topology Differential Geometry Dynamical Systems 57R30, 57T20 Let $M$ be a smooth manifold and $\mathcal{F}$ a Morse-Bott foliation on $M$ with a compact critical manifold $Σ$. Denote by $\mathcal{D}(\mathcal{F})$ the group of diffeomorphisms of $M$ leaving invariant each leaf of $\mathcal{F}$. Under certain assumptions on $\mathcal{F}$ it is shown that the computation of the homotopy type of $\mathcal{D}(\mathcal{F})$ reduces to three rather independent groups: the group of diffeomorphisms of $Σ$, the group of vector bundle automorphisms of some regular neighborhood of $Σ$, and the subgroup of $\mathcal{D}(\mathcal{F})$ consisting of diffeomorphisms fixed near $Σ$. Examples of computations of homotopy types of groups $\mathcal{D}(\mathcal{F})$ for such foliations are also presented. |
| title | Vector bundle automorphisms preserving Morse-Bott foliations |
| topic | Geometric Topology Algebraic Topology Differential Geometry Dynamical Systems 57R30, 57T20 |
| url | https://arxiv.org/abs/2311.13176 |