Algebraic topology: The Abel symposium 2007

John C. Baez, Danny Stevenson (auth.), Nils Baas, Eric M. Friedlander, Björn Jahren, Paul Arne Østvær (eds.)3642011993, 9783642011993

The 2007 Abel Symposium took place at the University of Oslo in August 2007. The goal of the symposium was to bring together mathematicians whose research efforts have led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology, and mathematical physics. A common theme of this symposium was the development of new perspectives and new constructions with a categorical flavor. As the lectures at the symposium and the papers of this volume demonstrate, these perspectives and constructions have enabled a broadening of vistas, a synergy between once-differentiated subjects, and solutions to mathematical problems both old and new.

Table of contents :
Front Matter….Pages 1-11
The Classifying Space of a Topological 2-Group….Pages 1-31
String Topology in Dimensions Two and Three….Pages 33-37
Floer Homotopy Theory, Realizing Chain Complexes by Module Spectra, and Manifolds with Corners….Pages 39-59
Relative Chern Characters for Nilpotent Ideals….Pages 61-82
Algebraic Differential Characters of Flat Connections with Nilpotent Residues….Pages 83-94
Norm Varieties and the Chain Lemma (After Markus Rost)….Pages 95-130
On the Whitehead Spectrum of the Circle….Pages 131-184
Cocycle Categories….Pages 185-218
A Survey of Elliptic Cohomology….Pages 219-277
On Voevodsky’s Algebraic K -Theory Spectrum….Pages 279-330
Chern Character, Loop Spaces and Derived Algebraic Geometry….Pages 331-354
Voevodsky’s Lectures on Motivic Cohomology 2000/2001….Pages 355-409