Homotopy types of diffeomorphisms groups of simplest Morse-Bott foliations on lens spaces, 2
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917644116951040 |
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| author | Maksymenko, Sergiy |
| author_facet | Maksymenko, Sergiy |
| contents | Let $\mathcal{F}$ be a Morse-Bott foliation on the solid torus $T=S^1\times D^2$ into $2$-tori parallel to the boundary and one singular central circle. Gluing two copies of $T$ by some diffeomorphism between their boundaries, one gets a lens space $L_{p,q}$ with a Morse-Bott foliation $\mathcal{F}_{p,q}$ obtained from $\mathcal{F}$ on each copy of $T$ and thus consisting of two singluar circles and parallel $2$-tori. In the previous paper [O. Khokliuk, S. Maksymenko, Journ. Homot. Rel. Struct., 2024, 18, 313-356] there were computed weak homotopy types of the groups $\mathcal{D}^{lp}(\mathcal{F}_{p,q})$ of leaf preserving (i.e. leaving invariant each leaf) diffeomorphisms of such foliations. In the present paper it is shown that the inclusion of these groups into the corresponding group $\mathcal{D}_{+}^{fol}(\mathcal{F}_{p,q})$ of foliated (i.e. sending leaves to leaves) diffeomorphisms which do not interchange singular circles are homotopy equivalences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12447 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homotopy types of diffeomorphisms groups of simplest Morse-Bott foliations on lens spaces, 2 Maksymenko, Sergiy Geometric Topology Algebraic Topology Differential Geometry Dynamical Systems 57R30, 57T20 Let $\mathcal{F}$ be a Morse-Bott foliation on the solid torus $T=S^1\times D^2$ into $2$-tori parallel to the boundary and one singular central circle. Gluing two copies of $T$ by some diffeomorphism between their boundaries, one gets a lens space $L_{p,q}$ with a Morse-Bott foliation $\mathcal{F}_{p,q}$ obtained from $\mathcal{F}$ on each copy of $T$ and thus consisting of two singluar circles and parallel $2$-tori. In the previous paper [O. Khokliuk, S. Maksymenko, Journ. Homot. Rel. Struct., 2024, 18, 313-356] there were computed weak homotopy types of the groups $\mathcal{D}^{lp}(\mathcal{F}_{p,q})$ of leaf preserving (i.e. leaving invariant each leaf) diffeomorphisms of such foliations. In the present paper it is shown that the inclusion of these groups into the corresponding group $\mathcal{D}_{+}^{fol}(\mathcal{F}_{p,q})$ of foliated (i.e. sending leaves to leaves) diffeomorphisms which do not interchange singular circles are homotopy equivalences. |
| title | Homotopy types of diffeomorphisms groups of simplest Morse-Bott foliations on lens spaces, 2 |
| topic | Geometric Topology Algebraic Topology Differential Geometry Dynamical Systems 57R30, 57T20 |
| url | https://arxiv.org/abs/2301.12447 |