幫助中心 | 我的帳號 | 關於我們

代數K理論及其應用(英文版)

  • 作者:(美)羅森博格|責編:劉慧//高蓉
  • 出版社:世界圖書出版公司
  • ISBN:9787510005145
  • 出版日期:2010/02/01
  • 裝幀:平裝
  • 頁數:392
人民幣:RMB 79 元      售價:
放入購物車
加入收藏夾

內容大鋼
    代數K理論在代數拓撲、數論、代數幾何和運算元理論等現代數學各個領域中的作用越來越大。這門學科的廣泛性往往使人感覺望而生畏。本書以1990年秋天Maryland大學講義為基礎,不僅為數學領域研究生提供很好的學習代數K理論的基本知識,也講述其在各個領域的應用。全書結構完整,了解代數基礎知識、基本代數拓撲和幾何拓撲知識就可以完全讀懂這本書。該書也涉及到不少代數拓撲、拓撲代數和代數數論的知識。最後一章簡明地介紹了循環同調以及其與K理論的關係。

作者介紹
(美)羅森博格|責編:劉慧//高蓉

目錄
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

  • 商品搜索:
  • | 高級搜索
首頁新手上路客服中心關於我們聯絡我們Top↑
Copyrightc 1999~2008 美商天龍國際圖書股份有限公司 臺灣分公司. All rights reserved.
營業地址:臺北市中正區重慶南路一段103號1F 105號1F-2F
讀者服務部電話:02-2381-2033 02-2381-1863 時間:週一-週五 10:00-17:00
 服務信箱:bookuu@69book.com 客戶、意見信箱:cs@69book.com
ICP證:浙B2-20060032