Homotopy types of diffeomorphism groups of polar Morse-Bott foliations on lens spaces, 1
| Autor: | Khokhliuk, Oleksandra, Maksymenko, Sergiy |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Homotopy and Related Structures, 18 (2023) 313-356 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s40062-023-00328-z |
| Popis: | Let $T= S^1\times D^2$ be the solid torus, $\mathcal{F}$ the Morse-Bott foliation on $T$ into $2$-tori parallel to the boundary and one singular circle $S^1\times 0$, which is the central circle of the torus $T$, and $\mathcal{D}(\mathcal{F},\partial T)$ the group of diffeomorphisms of $T$ fixed on $\partial T$ and leaving each leaf of the foliation $\mathcal{F}$ invariant. We prove that $\mathcal{D}(\mathcal{F},\partial T)$ is contractible. Gluing two copies of $T$ by some diffeomorphism between their boundaries, we will get a lens space $L_{p,q}$ with a Morse-Bott foliation $\mathcal{F}_{p,q}$ obtained from $\mathcal{F}$ on each copy of $T$. We also compute the homotopy type of the group $\mathcal{D}(\mathcal{F}_{p,q})$ of diffeomorphisms of $L_{p,q}$ leaving invariant each leaf of $\mathcal{F}_{p,q}$. Comment: 37 pages, 2 figures, the content is essentially reworked |
| Databáze: | arXiv |
| Externí odkaz: |
|