Algebraic Topology

The 2007 Abel Symposium brought together mathematicians whose research has led to recent advances in algebraic geometry, algebraic K-theory, algebraic topology and mathematical physics. This book offers the highlights of that symposium.

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.

Highlights of high-level symposium in the Abel Prize series

Résumé

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.

Contenu
The Classifying Space of a Topological 2-Group.- String Topology in Dimensions Two and Three.- Floer Homotopy Theory, Realizing Chain Complexes by Module Spectra, and Manifolds with Corners.- Relative Chern Characters for Nilpotent Ideals.- Algebraic Differential Characters of Flat Connections with Nilpotent Residues.- Norm Varieties and the Chain Lemma (After Markus Rost).- On the Whitehead Spectrum of the Circle.- Cocycle Categories.- A Survey of Elliptic Cohomology.- On Voevodsky#x0027;s Algebraic -Theory Spectrum.- Chern Character, Loop Spaces and Derived Algebraic Geometry.- Voevodsky#x0027;s Lectures on Motivic Cohomology 2000/2001.