The Brown-Peterson homology and nilpotence of the infinite special orthogonal group.
The computation of Stiefel-Whitney classes
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...
The cyclic homology of the group rings.
The Euler Characteristic is the Unique Locally Determined Numerical Homotopy Invariant of Finite Complexes.
The geometry of the local cohomology filtration in equivariant bordism.
The integral cohomology rings of real infinite-dimensional flag manifolds
The Mod 2 Cohomology Rings of Extra-special 2-groups and the Spinor Groups.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The Positvity of the Chern Classes of an Ample Vector Bundle.
The Signature mod 8
The Signature of Quasi-Nilpotent Fiber Bundles
The ...-Spectrum for Brown-Peterson Cohomology. Part I
The Universal Smooth Surgery Class.
The Weil algebra and the Van Est isomorphism
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 associated to any Lie algebroid . 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...
The Z*-theorem for compact Lie groups.
Transfer and complex oriented cohomology rings.