# Non-degenerescence of some spectral sequences

Annales de l'institut Fourier (1984)

- Volume: 34, Issue: 1, page 39-46
- ISSN: 0373-0956

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topSarkaria, K. S.. "Non-degenerescence of some spectral sequences." Annales de l'institut Fourier 34.1 (1984): 39-46. <http://eudml.org/doc/74620>.

@article{Sarkaria1984,

abstract = {Each Lie algebra $\{\cal F\}$ 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 $E_k(\{\cal F\})$ which converges to the de Rham cohomology of $M$ in a finite number of steps. We prove e.g. that for all $k\ge 0$ there exists a foliated compact manifold with $E_k(\{\cal F\})$ infinite dimensional.},

author = {Sarkaria, K. S.},

journal = {Annales de l'institut Fourier},

keywords = {Lie algebra of vector fields tangent to a foliation; spectral sequence converging to the de Rham cohomology},

language = {eng},

number = {1},

pages = {39-46},

publisher = {Association des Annales de l'Institut Fourier},

title = {Non-degenerescence of some spectral sequences},

url = {http://eudml.org/doc/74620},

volume = {34},

year = {1984},

}

TY - JOUR

AU - Sarkaria, K. S.

TI - Non-degenerescence of some spectral sequences

JO - Annales de l'institut Fourier

PY - 1984

PB - Association des Annales de l'Institut Fourier

VL - 34

IS - 1

SP - 39

EP - 46

AB - Each Lie algebra ${\cal F}$ 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 $E_k({\cal F})$ which converges to the de Rham cohomology of $M$ in a finite number of steps. We prove e.g. that for all $k\ge 0$ there exists a foliated compact manifold with $E_k({\cal F})$ infinite dimensional.

LA - eng

KW - Lie algebra of vector fields tangent to a foliation; spectral sequence converging to the de Rham cohomology

UR - http://eudml.org/doc/74620

ER -

## References

top- [1] A. FROHLICHER, Relations between the cohomology groups of Dolbeault and topological invariants, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), 641-644. Zbl0065.16502MR17,409a
- [2] P. GRIFFITHS and J. HARRIS, Principles of Algebraic Geometry, John Wiley and Sons, New York, 1978. Zbl0408.14001MR80b:14001
- [3] K.S. SARKARIA, A finiteness theorem for foliated manifolds, Jour. Math. Soc. Japan, 30 (1978), 687-696. Zbl0398.57012MR80a:57014
- [4] G. SCHWARZ, On the de Rham cohomology of the leaf space of a foliation, Topology, 13 (1974), 185-187. Zbl0282.57016MR49 #6254

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