- 纽结理论(英文版)(精)/美国数学会经典影印系列
- - 作者：(美)查尔斯·利文斯顿|责编:李华英
  - 出版社：高等教育
  - ISBN：9787040593075
  - 出版日期：2023/03/01
  - 页数：240
- 售价：54

内容大纲
这是一本生动的关于数学纽结的说明书，将吸引各式各样的读者，从寻求传统学习以外经验的本科生，到想要悠闲介绍这个主题的数学家。刚开始深入学习的研究生将会发现这是一份有价值的概述，读者只需要线性代数的训练，就可以理解书中提到的数学内容。当从线性代数和基本的群论中引入工具研究纽结的性质时，拓扑和代数之间的相互作用，即代数拓扑，在书中早早出现。
Livingston带领读者通过这个课题的概览，展示如何使用线性代数的技巧来解决一些复杂问题，包括数学中最美丽的主题之一：对称。本书最后讨论了高维纽结理论，以及该学科的一些最新进展，包括Conway、Jones和Kauffman的多项式。补充部分介绍了基本群，它是代数拓扑的核心。
作者介绍
目录
ACKNOWLEDGEMENTS
PREFACE
Chapter 1  A CENTURY OF KNOT THEORY
Chapter 2  WHAT Is A KNoT?
  Section 1  Wild Knots and Unknottings
  Section 2  The Definition of a Knot
  Section 3  Equivalence of Knots, Deformations
  Section 4  Diagrams and Projections
  Section 5  Orientations
Chapter 3  COMBINATORIAL TECHNIQUES
  Section 1  Reidemeister Moves
  Section 2  Colorings
  Section 3  A Generalization of Colorability, mod p Labelings
  Section 4  Matrices, Labelings, and Determinants
  Section 5  The Alexander Polynomial
Chapter 4  GEOMETRIC TECHNIQUES
  Section 1  Surfaces and Homeomorphisms
  Section 2  The Classification of Surfaces
  Section 3  Seifert Surfaces and the Genus of a Knot
  Section 4  Surgery on Surfaces
  Section 5  Connected Sums of Knots and Prime Decompositions
Chapter 5  ALGEBRAIC TECHNIQUES
  Section 1  Symmetric Groups
  Section 2  Knots and Groups
  Section 3  Conjugation and the Labeling Theorem
  Section 4  Equations in Groups and the Group of a Knot
  Section 5  The Fundamental Group
Chapter 6  GEOMETRY, ALGEBRA, AND THE ALEXANDER POLYNOMIAL
  Section 1  The Seifert Matrix
  Section 2  Seifert Matrices and the Alexander Polynomial
  Section 3  The Signature of a Knot, and other S-Equivalence Invariants
  Section 4  Knot Groups and the Alexander Polynomial
Chapter 7  NUMERICAL INVARIANTS
  Section 1  Summary of Numerical Invariants
  Section 2  New Invariants
  Section 3  Braids and Bridges
  Section 4  Relations Between the Numerical Invariants
  Section 5  Independence of Numerical Invariants
Chapter 8  SYMMETRIES OF KNOTS
  Section 1  Amphicheiral and Reversible Knots
  Section 2  Periodic Knots
  Section 3  The Murasugi Conditions
  Section 4  Periodic Seifert Surfaces and Edmonds' Theorem
  Section 5  Applications of the Murasugi and Edmonds Conditions
Chapter 9  HIGH-DIMENSIONAL KNOT THEORY
  Section 1  Defining High-dimensional Knots
  Section 2  Three Dimensions from a 2-dimensional Perspective
  Section 3  Three-dimensional Cross-sections of a 4-dimensional Knot
  Section 4  Slice Knots
  Section 5  The Knot Concordance Group

Chapter 10  NEw COMBINATORIAL TECHNIQUES
  Section 1  The Conway Polynomial of a Knot
  Section 2  New Polynomial Invariants
  Section 3  Kauffman's Bracket Polynomial
Appendix 1  KNOT TABLE
Appendix 2  ALEXANDER POLYNOMIALS
REFERENCES
INDEX

内容大纲

作者介绍

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