Extending regular foliations

J. W. Smith

Displaying similar documents to “Extending regular foliations”

Natural liftings of foliations to the $r$ -tangent bunde

Mikulski, Włodzimierz M.

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Let $F$ be a $p$ -dimensional foliation on an $n$ -manifold $M$ , and $T^{r} M$ the $r$ -tangent bundle of $M$ . The purpose of this paper is to present some reltionship between the foliation $F$ and a natural lifting of $F$ to the bundle $T^{r} M$ . Let $L_{q}^{r} (F)$ $(q = 0, 1, \dots, r)$ be a foliation on $T^{r} M$ projectable onto $F$ and $L_{q}^{r} = {L_{q}^{r} (F)}$ a natural lifting of foliations to $T^{r} M$ . The author proves the following theorem: Any natural lifting of foliations to the $r$ -tangent bundle is equal to one of the liftings $L_{0}^{r}, L_{1}^{r}, \dots, L_{n}^{r}$ . The exposition is clear and well organized. ...

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...

Correspondence between diffeomorphism groups and singular foliations

Tomasz Rybicki (2012)

Annales Polonici Mathematici

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It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation $ℱ_{G}$ . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^{r}$ diffeomorphism group G is simple iff the foliation $ℱ_{[G, G]}$ defined by [G,G] admits no proper...

Warped compact foliations

Szymon M. Walczak (2008)

Annales Polonici Mathematici

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The notion of the Hausdorffized leaf space $\tilde{}$ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to $\tilde{}$ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to $\tilde{}$ is shown. Finally, some examples are examined.

A splitting theorem for the Kupka component of a foliation of $ℂ ℙ^{n}, n \geq 6$ . Addendum to an addendum to a paper by Calvo-Andrade and Soares

Edoardo Ballico (1999)

Annales de l'institut Fourier

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Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of $ℂ ℙ^{n}, n \geq 6$ is a complete intersection. The result implies the existence of a meromorphic first integral of $F$ . The result was previously known if $\deg (K)$ was assumed to be not a square.

A splitting theorem for the Kupka component of a foliation of $𝐂 𝐏^{n}, n \geq 6$ . Addendum to a paper by O. Calvo-Andrade and N. Soares

Edoardo Ballico (1995)

Annales de l'institut Fourier

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Here we show that a Kupka component $K$ of a codimension 1 singular foliation $F$ of $C P^{n}, n \geq 6$ with $\deg (K)$ not a square is a complete intersection. The result implies the existence of a meromorphic first integral of $F$ .

Displaying similar documents to “Extending regular foliations”

Natural liftings of foliations to the r -tangent bunde

Foliations and spinnable structures on manifolds

Correspondence between diffeomorphism groups and singular foliations

Warped compact foliations

A splitting theorem for the Kupka component of a foliation of ℂ ℙ n , n ≥ 6 . Addendum to an addendum to a paper by Calvo-Andrade and Soares

A splitting theorem for the Kupka component of a foliation of 𝐂 𝐏 n , n ≥ 6 . Addendum to a paper by O. Calvo-Andrade and N. Soares

Natural liftings of foliations to the $r$ -tangent bunde

A splitting theorem for the Kupka component of a foliation of $ℂ ℙ^{n}, n \geq 6$ . Addendum to an addendum to a paper by Calvo-Andrade and Soares

A splitting theorem for the Kupka component of a foliation of $𝐂 𝐏^{n}, n \geq 6$ . Addendum to a paper by O. Calvo-Andrade and N. Soares