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Cohomologie tangente et cup-produit pour la quantification de Kontsevich

Dominique Manchon, Charles Torossian (2003)

Annales mathématiques Blaise Pascal

On a flat manifold M = ℝ d , M. Kontsevich’s formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that for any formal Poisson 2 -tensor ℏ γ the derivative at ℏ γ of the quasi-isomorphism induces an isomorphism of graded commutative algebras from Poisson cohomology space to Hochschild cohomology space relative to the deformed multiplication built from ℏ γ via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised....

Collapse of warped submersions

Szymon M. Walczak (2006)

Annales Polonici Mathematici

We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds ( M , g M ) and ( B , g B ) in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric g f on M by g f | × ≡ g M | × , g f | × T M ̂ ≡ f ̂ ² g M | × T M ̂ , where and denote the bundles of horizontal and vertical vectors. The manifold ( M , g f ) obtained that way is called a warped submersion. The function f is called a warping function. We show a necessary...

Collective geodesic flows

Léo T. Butler, Gabriel P. Paternain (2003)

Annales de l’institut Fourier

We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.

Combinatorial differential geometry and ideal Bianchi–Ricci identities II – the torsion case

Josef Janyška, Martin Markl (2012)

Archivum Mathematicum

This paper is a continuation of [2], dealing with a general, not-necessarily torsion-free, connection. It characterizes all possible systems of generators for vector-field valued operators that depend naturally on a set of vector fields and a linear connection, describes the size of the space of such operators and proves the existence of an ‘ideal’ basis consisting of operators with given leading terms which satisfy the (generalized) Bianchi–Ricci identities without corrections.

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