- 代数K理论及其应用(英文版)
- - 作者：(美)罗森博格|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787510005145
  - 出版日期：2010/02/01
  - 页数：392
- 售价：31.6

内容大纲
代数K理论在代数拓扑、数论、代数几何和算子理论等现代数学各个领域中的作用越来越大。这门学科的广泛性往往使人感觉望而生畏。本书以1990年秋天Maryland大学讲义为基础，不仅为数学领域研究生提供很好的学习代数K理论的基本知识，也讲述其在各个领域的应用。全书结构完整，了解代数基础知识、基本代数拓扑和几何拓扑知识就可以完全读懂这本书。该书也涉及到不少代数拓扑、拓扑代数和代数数论的知识。最后一章简明地介绍了循环同调以及其与K理论的关系。
作者介绍
目录
Preface
Chapter 1.Ko of Rings
  1.Defining K0
  2.Ko from idempotents
  3.Ko of PIDs and local rings
  4.Ko of Dedekind domains
  5.Relative Ko and excision
  6.An application: Swan's Theorem and topological K-theory
  7.Another application: Euler characteristics and the Wall finiteness obstruction
Chapter 2.K1 of Rings
  1.Defining K1
  2.K1 of division rings and local rings
  3.K1 of PIDs and Dedekind domains
  4.Whitehead groups and Whitehead torsion
  5.Relative K1 and the exact sequence
Chapter 3.Ko and K1 of Categories, Negative K-Theory
  1.Ko and K1 of categories, Go and G1 of rings
  2.The Grothendieck and Bass-Heller-Swan Theorems
  3.Negative K-theory
Chapter 4.Milnor's K2
  1.Universal central extensions and H2
    Universal central extensions
    Homology of groups
  2.The Steinberg group
  3.Milnor's K2
  4.Applications of K2
    Computing certain relative K1 groups
    K2 of fields and number theory
    Almost commuting operators
    Pseudo-isotopy
Chapter 5.The +-Construction and Quillen K-Theory
  1.An introduction to classifying spaces
  2.Quillen's +-construction and its basic properties
  3.A survey of higher K-theory
    Products
    K-theory of fields and of rings of integers
    The Q-construction and results proved with it
    Applications
Chapter 6.Cyclic homology and its relation to K-Theory
  1.Basics of cyclic homology
    Hochschild homology
    Cyclic homology
    Connections with "non-commutative de Rhom theory"
  2.The Chern character
    The classical Chern character
    The Chern character on Ko
    The Chern character on higher K-theory
  3.Some applications
    Non-vanishing of class groups and Whitehead groups
    Idempotents in C*-algebras

    Group rings and assembly maps
References
  Books and Monographs on Related Areas of Algebra,Analysis, Number Theory, and Topology
  Books and Monographs on Algebraic K-Theory
  Specialized References
Notational Index
Subject Index

内容大纲

作者介绍

目录

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