Cohomological Methods in Homotopy Theory Barcelona Conference on Algebraic Topology, Bellatera, Spain, June 4–10, 1998

This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the occasion of an emphasis semester organized by the Centre de Recerca Matem?tica in Bellaterra (Barcelona) in 1998. The main topics treated in the book include abstract features of stable and unstable homotopy, homotopical localizations, p-compact groups, H-spaces, classifying spaces for proper actions, cohomology of discrete groups, K-theory and other generalized cohomology theories, configuration spaces, and Lusternik-Schnirelmann category.The book is addressed to all mathematicians interested in homotopy theory and in geometric aspects of group theory. New research directions in topology are highlighted. Moreover, this informative and educational book serves as a welcome reference for many new results and recent methods.

Etale approximations and the mod l cohomology of GLn.- On the Hurewicz map and Postnikov invariants of K?.- Recognition principle for generalized Eilenberg—Mac Lane spaces.- Groups with infinite homology.- Unstable splittings related to Brown—Peterson cohomology.- Stripping and splitting decorated mapping class groups.- Loop spaces of configuration spaces, braid-like groups, and knots.- On the homotopy type of infinite stunted projective spaces.- Stable splittings of ?SU(n).- Structure of mod p H-spaces with finiteness conditions.- Composition methods in the homotopy groups of ring spectra.- Tate cohomology in axiomatic stable homotopy theory.- Serre’s theorem and the Nill filtration of Lionel Schwartz.- New relationships among loopspaces, symmetric products, and Eilenberg MacLane spaces.- Chern characters for the equivariant K-theory of proper G-CW-complexes.- The Thomified Eilenberg—Moore spectral sequence.- On the classifying space for proper actions.- Toric morphisms between p-compact groups.- On the vanishing of certain K-theory Nil-groups.- Lusternik-Schnirelmann cocategory: A Whitehead dual approach.- Rational self-equivalences for H-spaces.- Cellular approximations using Moore spaces.- Configuration spaces with summable labels.- Kaleidoscoping Lusternik—Schnirelmann category type invariants.- Essential category weight and phantom maps.