We describe the fundamental properties of the infinitesimal actions related with functorial prolongations of principal and associated bundles with respect to fiber product preserving bundle functors. Our approach is essentially based on the Weil algebra technique and an original concept of weak principal bundle.
En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.
We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the fixed point case (known as Zung’s theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passage to general orbits (Weinstein) is given a more conceptual interpretation: as a manifestation of Morita invariance. We also clarify the precise statements of the Linearization Theorem (there has been some confusion on this, which has propagated throughout...
In this paper we study the real secondary classes of transversely holomorphic foliations. We define a homomorphism from the space of the real secondary classes to the space of the complex secondary classes that corresponds to forgetting the transverse holomorphic structure. By using this homomorphism we show, for example, the decomposition of the Godbillon-Vey class into the imaginary part of the Bott class and the first Chern class of the complex normal bundle of the foliation. We show also...