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 ⊂ 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 , ⋯ , 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 , ⋯ , 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 × ( 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 ˜ of a foliation is introduced. A sufficient condition for warped compact foliations to converge to ˜ is given. Moreover, a necessary condition for warped compact Hausdorff foliations to converge to ˜ 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 .

Foliations by complex manifolds involving the complex Hessian

Julian Ławrynowicz, Jerzy Kalina, Masami Okada

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SummaryIn 1979 the second named author proved, in a joint paper with J. Ławrynowicz, the existence of a foliation of a bounded domain in ℂ n by complex submanifolds of codimension k+p-1, connected in some sense with a real (1,1) C³-form of rank k and the pth power of the complex Hessian of a C³-function u with im u plurisubharmonic and the property that for every leaf of this foliation the restricted functions im u, re u and ( ∂ / ∂ z j ) i m u , ( ∂ / ∂ z j ) r e u are pluriharmonic and holomorphic, respectively.Now the...