Cohomology of Groups and Algebraic K-theory (Advanced Lectures in Mathematics)

Cohomology of groups is a fundamental tool in many subjects of modern mathematics. One important generalized cohomology theory is the algebraic K-theory. Indeed, algebraic K-groups of rings are important invariants of the rings and have played important roles in algebra, topology, number theory, etc. This volume consists of expanded lecture notes from a 2007 seminar at Zhejiang University in China, at which several leading experts presented introductions, to and surveys of, many aspects of cohomology of groups and algebraic K-theory, along with their broad applications. Two foundational papers on algebraic K-theory by Daniel Quillen are also included. Table of Contents: On Crossed Product Rings with Twisted Involutions, Their Module Categories and L-Theory - Arthur Bartels and Wolfgang Lück; Deformation Spaces for Affine Crystallographic Groups - Oliver Baues; Lectures on the Cohomology of Groups - Kenneth S. Brown; A Brief Introduction to Algebraic K-Theory - Daniel R. Grayson; The Braid Groups of RP2 Satisfy the Fibered Isomorphism Conjecture - Daniel Juan-Pineda and Silvia Millan-López; K-Theory, an Elementary Introduction - Max Karoubi ; Lectures on K-Theory - Max Karoubi; On the Farrell-Jones and Related Conjectures - Wolfgang Lück; Introduction to Controlled Topology and its Applications - Stratos Prassidis; Lecture Notes on K-Theory - Hourong Qin; Higher Algebraic K-Theory: I - Daniel Quillen; Finite Generation of the Groups Ki of Rings of Algebraic Integers - Daniel Quillen; A User’s Guide to Continuously Controlled Algebra - David Rosenthal; Higher K-Theory of Algebraic Integers and the Cohomology of Arithmetic Groups - Christophe Soulé (Notes by Marco Varisco).