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The wave map problem. Small data critical regularity

Igor Rodnianski (2005/2006)

Séminaire Bourbaki

The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is ( 2 + 1 ) , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory. As a consequence,...

The wedge sum of differential spaces

Sasin, Wiesław (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]Differential spaces, whose theory was initiated by R. Sikorski in the sixties, provide an abstract setting for differential geometry. In this paper the author studies the wedge sum of such spaces and deduces some basic results concerning this construction.

The Weil algebra and the Van Est isomorphism

Camilo Arias Abad, Marius Crainic (2011)

Annales de l’institut Fourier

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 conceptual...

Théorie de jauge et symétries des fibrés

D. Brandt, Jean-Claude Hausmann (1993)

Annales de l'institut Fourier

Soit ξ un G -fibré principal différentiable sur une variété M ( G un groupe de Lie compact). Étant donné une action d’un groupe de Lie compact Γ sur M , on se pose la question de savoir si elle provient d’une action sur le fibré ξ . L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de Γ que l’on induit naturellement sur divers espaces de modules de G -connexions sur ξ .

Theory of coverings in the study of Riemann surfaces

Ewa Tyszkowska (2012)

Colloquium Mathematicae

For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method...

Currently displaying 361 – 380 of 488