Homotopy types of diffeomorphism groups of polar Morse–Bott foliations on lens spaces, 2

IF 0.7 4区 数学 Q2 MATHEMATICS
Sergiy Maksymenko
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引用次数: 0

Abstract

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 singular circles and parallel 2-tori. In the previous paper Khokliuk and Maksymenko (J Homotopy Relat Struct 18:313–356. https://doi.org/10.1007/s40062-023-00328-z, 2024) 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.

透镜空间上极性莫尔斯-波特叶形的差分群的同调类型,2
让 \({\mathcal {F}}\) 是实体环 \(T=S^1\times D^2\) 上的莫尔斯-鲍特(Morse-Bott)折射,分为与边界平行的两个蝶形和一个奇异的中心圆。把两个 T 的副本通过它们边界之间的某种差分变形粘合起来,就会得到一个透镜空间 \(L_{p,q}\),其中每个 T 的副本上都有一个从 \({\mathcal {F}}/{p,q}\)得到的 Morse-Bott foliation \({\mathcal {F}}_{p,q}\),因此由两个奇异的圆和平行的 2-tori 组成。在之前的论文 Khokliuk 和 Maksymenko (J Homotopy Relat Struct 18:313-356. https://doi.org/10.1007/s40062-023-00328-z, 2024) 中,计算了这种叶形的叶保留(即每个叶保持不变)差分同构群 \({\mathcal {D}}^{lp}({\mathcal {F}}_{p,q}) 的弱同构类型。本文证明了这些群包含在不交换奇异圆的叶保留(即把叶送到叶)衍射的相应群 \({\mathcal {D}^{fol}_{+}({\mathcal {F}}_{p,q}) 中是同调等价的。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
21
审稿时长
>12 weeks
期刊介绍: Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
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