Non-degenerescence of some spectral sequences

K. S. Sarkaria

Displaying similar documents to “Non-degenerescence of some spectral sequences”

Extending regular foliations

J. W. Smith (1969)

Annales de l'institut Fourier

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A $p$ -dimensional foliation $F$ on a differentiable manifold $M$ is said to extend provided there exists a $(p + 1)$ -dimensional foliation $F^{'}$ on $M$ with $F \subset F^{'}$ . Our main result asserts that if $M$ and $F$ extends over relatively compact subsets of $M$ .

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. ...

On the Cech bicomplex associated with foliated structures

Haruo Kitahara, Shinsuke Yorozu (1978)

Annales de l'institut Fourier

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For a codimension $q$ foliation on a manifold, $η \times (d η)^{q}$ defines the Godbillon-Vey class. We show that $η$ itself defines a certain cohomology class, via the Cech bicomplex.

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.

Foliations with complex leaves

Giuliana Gigante, Giuseppe Tomassini (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $X$ be a smooth foliation with complex leaves and let $D$ be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space $(X, D)$ . In particular we concentrate on the following two themes: function theory for the algebra $D (X)$ and cohomology with values in $D$ .

Displaying similar documents to “Non-degenerescence of some spectral sequences”

Extending regular foliations

Natural liftings of foliations to the r -tangent bunde

On the Cech bicomplex associated with foliated structures

Correspondence between diffeomorphism groups and singular foliations

Warped compact foliations

Foliations with complex leaves

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