Equivariant map

About: Equivariant map is a research topic. Over the lifetime, 9205 publications have been published within this topic receiving 137115 citations.

Gerbes on complex reductive Lie groups

Abstract: We construct a gerbe over a complex reductive Lie group G attached to an invariant bilinear form on a maximal diagonalizable subalgebra which is Weyl group invariant and satisfies a parity condition. By restriction to a maximal compact subgroup K, one then gets a gerbe over K. For a simply-connected group, the parity condition is the same used by Pressley and Segal; in general, it was introduced by Deligne and the author. The gerbe is defined by geometric methods, using the so-called Grothendieck manifold. It is equivariant under the conjugation action of G; its restriction to a semisimple orbit is not always trivial. The paper starts with a discussion of gerbe data (in the sense of Chatterjee and Hitchin) and of gerbes as geometric objects (sheaves of groupoids); the relation between the two approaches is presented. There is an Appendix on equivariant gerbes, discussed from both points of view.

Equivariant Pontrjagin Classes and Applications to Orbit Spaces

Abstract: L-classes of rational homology manifolds.- L-classes of symmetric froducts.- The G-signature theorem and some elementary number theory.

Universal Abelian covers of rational surface singularities and multi-index filtrations

Abstract: In previous papers, the authors computed the Poincare series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincare series were expressed as the integer parts of certain fractional power series, whose interpretation was not given. In this paper, we show that, up to a simple change of variables, these fractional power series are reductions of the equivariant Poincare series for filtrations on the ring of germs of functions on the universal Abelian cover of the surface. We compute these equivariant Poincare series.

Twisted K-theory – old and new

Abstract: Twisted K-theory has its origins in the author's PhD thesis (27) and in a paper with P. Donovan (19). The objective of this paper is to revisit the subject in the light of new developments inspired by Mathematical Physics. See for instance E. Witten (42), J. Rosenberg (37), C. Laurent-Gentoux, J.-L. Tu, P. Xu (41) and M.F. Atiyah, G. Segal (8), among many authors. We also prove some new results in the subject: a Thom isomorphism, explicit computations in the equivariant case and new cohomology operations.