Displaying similar documents to “On the cohomology of vector fields on parallelizable manifolds”

Second cohomology classes of the group of C 1 -flat diffeomorphisms

Tomohiko Ishida (2012)

Annales de l’institut Fourier

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We study the cohomology of the group consisting of all C ∞ -diffeomorphisms of the line, which are C 1 -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.

Geometry of third order ODE systems

Alexandr Medvedev (2010)

Archivum Mathematicum

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We compute cohomology spaces of Lie algebras that describe differential invariants of third order ordinary differential equations. We prove that the algebra of all differential invariants is generated by 2 tensorial invariants of order 2, one invariant of order 3 and one invariant of order 4. The main computational tool is a Serre-Hochschild spectral sequence and the representation theory of semisimple Lie algebras. We compute differential invariants up to degree 2 as application. ...

The Weil algebra and the Van Est isomorphism

Camilo Arias Abad, Marius Crainic (2011)

Annales de l’institut Fourier

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This paper belongs to a series of papers devoted to the study of the cohomology of classifying spaces. Generalizing the Weil algebra of a Lie algebra and Kalkman’s BRST model, here we introduce the Weil algebra W ( A ) associated to any Lie algebroid A . We then show that this Weil algebra is related to the Bott-Shulman complex (computing the cohomology of the classifying space) via a Van Est map and we prove a Van Est isomorphism theorem. As application, we generalize and find a simpler more...

Transgression and Clifford algebras

Rudolf Philippe Rohr (2009)

Annales de l’institut Fourier

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Let W be a differential (not necessarily commutative) algebra which carries a free action of a polynomial algebra S P with homogeneous generators p 1 , ⋯ , p r . We show that for W acyclic, the cohomology of the quotient H ( W / < p 1 , ⋯ , p r > ) is isomorphic to a Clifford algebra Cl ( P , B ) , where the (possibly degenerate) bilinear form B depends on W . This observation is an analogue of an old result of Borel in a non-commutative context. As an application, we study the case of W given by the quantized Weil algebra...