The Theory of Fixed Point Classes（英文影印版）（硬皮精装）
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- 原书名：The Theory of Fixed Point Classes
- 作者： Kiang Tsai-han
- 丛书名： 精装英文影印数学系列丛书
- 出版社：科学出版社
- ISBN：7030073290
- 上架时间：2006-8-18
- 出版日期：2006 年8月
- 开本：B5
- 页码：174
- 版次：1-1
- 所属分类：
数学 > 文科、经管、金融、工程数学 > 经济数学
内容简介回到顶部↑
the theory of fixed point classes (also known as nielsen fixed point theory) examines the fixed points of an arbitrary mapping of any connected finite polyhedron into itself. its main problem is to determine a lower bound of the geometric countings (i. e. the actual numbers) of fixed points of all mappings homotopic to the given mapping. the existence problem of fixed points is evidently a particular case. .
the present book is an english translation of the revised second chinese edition. it is a fundamental representation of the important theory, presented in a more elementary and geometric way than the existing literature. thus, it will serve as a good introduction to algebraic topology and geometry. ...
the present book is an english translation of the revised second chinese edition. it is a fundamental representation of the important theory, presented in a more elementary and geometric way than the existing literature. thus, it will serve as a good introduction to algebraic topology and geometry. ...
目录回到顶部↑
chapter i. the general problem. a particular case. a few historical remarks
introduction.
a. integral power mappings of the circle
1. integral power mappings. the lefschetz number and fixed points
2. exponential mappings. liftings of integral power mappings
3. fixed points of liftings. lifting classes and fixed point classes
b. general self-mapping of the circle
4. index or algebraic counting of an isolated fixed point
5. liftings of a self-mapping. homotopic self-mapping classes. fixed points of liftings
6. theorem l for the circle
7. lifting classes. fixed point classes
8. index of a fixed point class. the nielsen number. theorem n for the circle
c. a sketch of the theory of fixed point classes. a few historical remarks
9. from particular case to theory of fixed point classes
10. a few historical remarks
(1) the problem of existence or non-existence of fixed points
(2) the problem of the least number of fixed points
chapter ii. the nielsen number
1. lifting class and fixed point class
2. nonempty fixed point class. equivalent definition. finiteness
introduction.
a. integral power mappings of the circle
1. integral power mappings. the lefschetz number and fixed points
2. exponential mappings. liftings of integral power mappings
3. fixed points of liftings. lifting classes and fixed point classes
b. general self-mapping of the circle
4. index or algebraic counting of an isolated fixed point
5. liftings of a self-mapping. homotopic self-mapping classes. fixed points of liftings
6. theorem l for the circle
7. lifting classes. fixed point classes
8. index of a fixed point class. the nielsen number. theorem n for the circle
c. a sketch of the theory of fixed point classes. a few historical remarks
9. from particular case to theory of fixed point classes
10. a few historical remarks
(1) the problem of existence or non-existence of fixed points
(2) the problem of the least number of fixed points
chapter ii. the nielsen number
1. lifting class and fixed point class
2. nonempty fixed point class. equivalent definition. finiteness
前言回到顶部↑
Since the publication of the 1979 Chinese edition of the book Theory of Fixed Point Classes, my colleagues and I have used it as a major reference book in several seminars for beginning graduate students. When we began to revise it, our publishers proposed to translate it into English. We finally agreed that the author would translate the forthcoming revised Chinese edition. We explain here how the revised Chinese edition differs from the first Chinese edition and the English version from the revised. .
The revised edition contains no new material except for a few further developments of some topics already treated in the firstChinese edition. A number of typographic and minor errors have been corrected, some new examples added, and numerous improvements on representation have been introduced. ..
In the English version, Appendix D and the well-known examples and proofs in the Appendices A and B of the revised Chinese edition are omitted, for they are easily accessible in the English literature.
The author wishes to express his gratitude to his colleagues and students for all their help in preparing the manuscripts of these three editions. For this English version in particular, gratitude is also extended to Prof. Jiang Boju for reviewing the manuscript, to Mr. Chang Huicuan for proofreading and compiling the index and the list of symbols, and to Springer-Verlag and to Science Press for English language assistance. ...
Peking University Kiang Tsai-han
August 1987
The revised edition contains no new material except for a few further developments of some topics already treated in the firstChinese edition. A number of typographic and minor errors have been corrected, some new examples added, and numerous improvements on representation have been introduced. ..
In the English version, Appendix D and the well-known examples and proofs in the Appendices A and B of the revised Chinese edition are omitted, for they are easily accessible in the English literature.
The author wishes to express his gratitude to his colleagues and students for all their help in preparing the manuscripts of these three editions. For this English version in particular, gratitude is also extended to Prof. Jiang Boju for reviewing the manuscript, to Mr. Chang Huicuan for proofreading and compiling the index and the list of symbols, and to Springer-Verlag and to Science Press for English language assistance. ...
Peking University Kiang Tsai-han
August 1987
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