Diffeomorphisms preserving Morse-Bott functions
| Autor: | Khokhliuk, Oleksandra, Maksymenko, Sergiy |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Indagationes Mathematicae, vol. 31, no. 2 (2020) 185-203 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.indag.2019.12.004 |
| Popis: | Let $f:M\to\mathbb{R}$ be a Morse-Bott function on a closed manifold $M$, so the set $\Sigma_f$ of its critical points is a closed submanifold whose connected components may have distinct dimensions. Denote by $\mathcal{S}(f) = \{h \in \mathcal{D}(M) \mid f\circ h=h \}$ the group of diffeomorphisms of $M$ preserving $f$ and let $\mathcal{D}(\Sigma_f)$ be the group of diffeomorphisms of $\Sigma_f$. We prove that the "restriction to $\Sigma_f$" map $\rho:\mathcal{S}(f) \to \mathcal{D}(\Sigma_f)$, $\rho(h) = h|_{\Sigma_f}$, is a locally trivial fibration over its image $\rho(\mathcal{S}(f))$. Comment: 18 pages, the paper is published and we only updated the metadata |
| Databáze: | arXiv |
| Externí odkaz: |
|