Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the -theory of the corresponding reduced -algebras. Our proofs do not depend on the Baum–Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.
Any 7-dimensional cocalibrated -manifold admits a unique connection with skew symmetric torsion (see [8]). We study these manifolds under the additional condition that the -Ricci tensor vanish. In particular we describe their geometry in case of a maximal number of -parallel vector fields.
We give a necessary and sufficient condition for a Codazzi structure to be realized as a minimal affine hypersurface or a minimal centroaffine immersion of codimension two.
We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.
Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold . We show that if the fundamental group of each leaf of is isomorphic to , then is without holonomy. We also show that if and the fundamental group of each leaf of is isomorphic to (), then is without holonomy.
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
We study real submanifolds of a complex hyperbolic space and prove a codimension reduction theorem.
Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.
On a flat manifold , M. Kontsevich’s formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that for any formal Poisson -tensor the derivative at 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 via the quasi-isomorphism. We give here a detailed proof of this result, with signs and orientations precised....