点击选择搜索分类
首页 - 矿业工程- 正文
☆☆☆☆☆
||
[美] 罗森博格 著
出版社: 世界图书出版公司 ISBN:9787510005145 版次:1 商品编码:10515947 包装:平装 外文名称:Algebraic K-Theory and Its Applications 开本:24开 出版时间:2010-01-01 用纸:胶版纸 页数:392 正文语种:英文
读者对象:数学系高年级学生及研究生的教材,也可供高校数学教师及数学研究人员阅读或参考。
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: Swans 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. Milnors K2
1. Universal central extensions and H2
Universal central extensions
Homology of groups
2. The Steinberg group
3. Milnors 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. Quillens +-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
代数K理论及其应用 [Algebraic K-Theory and Its Applications] 电子书 下载 mobi epub pdf txt
代数K理论及其应用 [Algebraic K-Theory and Its Applications]-so88
代数K理论及其应用 [Algebraic K-Theory and Its Applications] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[美] 罗森博格 著
出版社: 世界图书出版公司 ISBN:9787510005145 版次:1 商品编码:10515947 包装:平装 外文名称:Algebraic K-Theory and Its Applications 开本:24开 出版时间:2010-01-01 用纸:胶版纸 页数:392 正文语种:英文
内容简介
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。《代数K理论及其应用》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《代数K理论及其应用》。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。目次:环的K0群;环的K1群;范畴的K0、K1群,MilnorK2群;QuillenK理论和+-结构;循环同调及其与K理论的关系。读者对象:数学系高年级学生及研究生的教材,也可供高校数学教师及数学研究人员阅读或参考。
目录
PrefaceChapter 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: Swans 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. Milnors K2
1. Universal central extensions and H2
Universal central extensions
Homology of groups
2. The Steinberg group
3. Milnors 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. Quillens +-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
前言/序言
代数K理论及其应用 [Algebraic K-Theory and Its Applications] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 一口气读懂常识丛书:一口气读懂化学常识 《一口气读懂化学常识》编写组
- 落叶跳舞 蒲蒲兰绘本馆 3~6岁儿童绘本 亲子读物 二十一世纪出版社 【新华书店正版书籍】
- 应急科普丛书:震后防疫常识
- 全4册蔷薇别墅的老鼠 书本里蚂蚁 王一梅童话系列故事书注音版 王一梅获奖童话文学阅读书籍
- 地理之 9787222153448
- 心理营养:林文采博士的亲子教育课
- 2016-2017-稀土科学技术学科发展报告
- 贴进大自然第1辑(套装共6册) [3-6岁]
- 对决系列--世界经典航空母舰对决
- 诊断医学寄生虫学-第5版
- 神秘的大脑:每天30秒探索令人兴奋的50个神经科学理念 科普读物 书籍
- 儿童口腔科临床技术手册 医学 书籍
- 狡猾的发明 震撼的装备 [英]格里贝利
- 预售社交恐怖症的森田疗法+强迫症的森田疗法+抑郁症的森田疗法+顺其自然的森田疗法中国森田疗
- 世界冲锋枪:Ⅰ 9787516501252