On the first homology of automorphism groups of manifolds with geometric structures

Kōjun Abe; Kazuhiko Fukui

Displaying similar documents to “On the first homology of automorphism groups of manifolds with geometric structures”

A classification of the topological types of $𝐑^{2}$ -actions on closed orientable 3-manifolds

Gilles Chatelet, Harold Rosenberg, Daniel Weil (1974)

Publications Mathématiques de l'IHÉS

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Smoothability of proper foliations

John Cantwell, Lawrence Conlon (1988)

Annales de l'institut Fourier

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Compact, $C^{2}$ -foliated manifolds of codimension one, having all leaves proper, are shown to be $C^{\infty}$ -smoothable. More precisely, such a foliated manifold is homeomorphic to one of class $C^{\infty}$ . The corresponding statement is false for foliations with nonproper leaves. In that case, there are topological distinctions between smoothness of class $C^{r}$ and of class $C^{r + 1}$ for every nonnegative integer $r$ .

Foliations with few non-compact leaves.

Vogt, Elmar (2002)

Algebraic & Geometric Topology

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Foliations with all leaves compact

D. B. A. Epstein (1976)

Annales de l'institut Fourier

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The notion of the “volume" of a leaf in a foliated space is defined. If $L$ is a compact leaf, then any leaf entering a small neighbourhood of $L$ either has a very large volume, or a volume which is approximatively an integral multiple of the volume of $L$ . If all leaves are compact there are three related objects to study. Firstly the topology of the quotient space obtained by identifying each leaf to a point ; secondly the holonomy of a leaf ; and thirdly whether the leaves have a locally...

Some properties of foliations

Richard Sacksteder (1964)

Annales de l'institut Fourier

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A foliation of $𝐑^{3}$ and other punctured 3-manifolds by circles

Elmar Vogt (1989)

Publications Mathématiques de l'IHÉS

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Leafwise smoothing laminations.

Calegari, Danny (2001)

Algebraic & Geometric Topology

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Foliations and spinnable structures on manifolds

Itiro Tamura (1973)

Annales de l'institut Fourier

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In this paper we study a new structure, called a spinnable structure, on a differentiable manifold. Roughly speaking, a differentiable manifold is spinnable if it can spin around a codimension 2 submanifold, called the axis, as if the top spins. The main result is the following: let $M$ be a compact $(n - 1)$ -connected $(2 n + 1)$ -dimensional differentiable manifold $(n \geq 3)$ , then $M$ admits a spinnable structure with axis $S^{2 n + 1}$ . Making use of the codimension-one foliation on $S^{2 n + 1}$ , this yields that $M$ admits...