from International Press

Advanced Lectures in Mathematics, Vol. 12

Cohomology of Groups and Algebraic K-theory

Edited by
Lizhen Ji (University of Michigan)
Kefeng Liu (University of California at Los Angeles)
Shing-Tung Yau (Harvard University)

Publication Details

Softcover. 517 pages.
ISBN: 978-1-57146-144-5
Published: March 2010
Publisher: International Press of Boston
List price: $65.00. Discounts may apply.

Full Description

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 K_i 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)

About the Series

Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cutting-edge results.

Other volumes in the Advanced Lectures in Mathematics series

Vol. 11. Recent Advances in Geometric Analysis

Vol. 10. Trends in Partial Differential Equations

Vol. 9. Automorphic Forms and the Langlands Program

Vol. 8. Recent Developments in Algebra and Related Areas

Vol. 7. Handbook of Geometric Analysis, No. 1

Vol. 6. Geometry, Analysis and Topology of Discrete Groups

Vol. 5. Fourth International Congress of Chinese Mathematicians (2007)

Vol. 4. Variational Principles for Discrete Surfaces

Vol. 3. Computational Conformal Geometry

Vol. 2. Asymptotic Theory in Probability and Statistics with Applications

Vol. 1. Superstring Theory

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