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 , ⋯ , 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. ...

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 ≥ 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 ˜ 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.

Non-degenerescence of some spectral sequences

K. S. Sarkaria (1984)

Annales de l'institut Fourier

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Each Lie algebra ℱ of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold M définies, in a natural way, a spectral sequence E k ( ℱ ) which converges to the de Rham cohomology of M in a finite number of steps. We prove e.g. that for all k ≥ 0 there exists a foliated compact manifold with E k ( ℱ ) infinite dimensional.