拓扑与几何

所属分类:数学  
出版时间:2008-1   出版时间:北京世图   作者:布里登   页数:557  
Tag标签:数学,Topology,几何与拓扑,Mathematics,拓扑学  

内容概要

This time of writing is the hundredth anniversary of the publication (1892) of Poincare's first note on topology, which arguably marks the beginning of the subject of algebraic, or "combinatorial," topology. There was earlier scattered work by Euler, Listing (who coined the word "topology"), M/Sbius and his band, Riemann, Klein, and Betti. Indeed, even as early as 1679, Leibniz indicated the desirability of creating a geometry of the topological type. The establishment of topology (or "analysis situs" as it was often called at the time) as a coherent theory, however, belongs to Poincar6.    Curiously, the beginning of general topology, also called "point settopology," dates fourteen years later when Fr6chet published the first abstract  treatment of the subject in 1906.   Since the beginning of time, or at least the era of A'rchimedes, smooth manifolds (curves, surfaces, mechanical configurations, the universe) have been a central focus in mathematics. They have always been at the core of interest in topology. After the seminal work of Milnor, Smale, and many others, in the last half of this century, the topological aspects of smooth manifolds, as distinct from the differential geometric aspects, became a subject in its own right. While the major portion of this book is devoted to algebraic topology, I attempt to give the reader some glimpses into the beautiful and important realm of smooth manifolds along the way, and to instill the tenet that the algebraic tools are primarily intended for the understanding of the geometric world.

作者简介

作者:(美国)布里登

书籍目录

PrefaceAcknowledgmentsCHAPTER
I General
Topology
1.
Metric
Spaces
2.
Topological
Spaces
3.
Subspaces
4.
Connectivity
and
Components
5.
Separation
Axioms
6.
Nets
(Moore-Smith
Convergence)
7.
Compactness
8.
Products
9.
Metric
Spaces
Again 10.
Existence
of
Real
Valued
Functions 11.
Locally
Compact
Spaces 12.
Paracompact
Spaces 13.
Quotient
Spaces
 14.
Homotopy 15.
Topological
Groups 16.
Convex
Bodies 17.
The
Baire
Category
TheoremCHAPTER
II Differentiable
Manifolds
1.
The
Implicit
Function
Theorem
2.
Differentiable
Manifolds
3.
Local
Coordinates 4.
Induced
Structures
and
Examples
5.
Tangent
Vectors
and
Differentials
6.
Sard's
Theorem
and
Regular
Values
7.
Local
Properties
of
Immersions
and
Submersions
8.
Vector
Fields
and
Flows
9.
Tangent
Bundles
10.
Embedding
in
Euclidean
Space
11.
Tubular
Neighborhoods
and
Approximations
12.
Classical
Lie
Groups
13.
Fiber
Bundles
14.
Induced
Bundles
and
Whitney
Sums
15.
Transversality
16.
Thom-Pontryagin
Theory
CHAPTER
III
Fundamental
Group
1.
Homotopy
Groups
2.
The
Fundamental
Group
3.
Covering
Spaces
4.
The
Lifting
Theorem
5.
The
Action
of
nl
on
the
Fiber
6.
Deck
Transformations
7.
Properly
Discontinuous
Actions
8.
Classification
of
Covering
Spaces
9.
The
Seifert-Van
Kampen
Theorem
10.
Remarks
on
SO(3)
CHAPTER
IV
Homology
Theory
1.
Homology
Groups
2.
The
Zeroth
Homology
Group
3.
The
First
Homology
Group
4.
Functorial
Properties
5.
Homological
Algebra
6.
Axioms
for
Homology
7.
Computation
of
Degrees
8.
CW-Complexes
9.
Conventions
for
CW-Complexes
10.
Cellular
Homology
11.
Cellular
Maps
12.
Products
of
CW-Complexes
13.
Euler's
Formula
14.
Homology
of
Real
Projective
Space
15.
Singular
Homology
16.
The
Cross
Product
17.
Subdivision
18.
The
Mayer-Vietoris
Sequence
19.
The
Generalized
Jordan
Curve
Theorem
20.
The
Borsuk-Ulam
Theorem
21.
Simplicial
Complexes……CHAPTER
V
CohomologyCHAPTER
VI
Products
and
DualityCHAPTER
VII
Homotopy
theoryAppendicesBibliographyIndex
of
SymbolsIndex

编辑推荐

本书是一部比较原始但又不失趣味性的拓扑与几何课本,完全是从现代观点研究问题,可以说是25年以来,继Spanier之后真正的一本全新的拓扑书。很适合作为一年级研究生的代数拓扑教科书。内容安排紧凑、合理,从一般拓扑开始,讲述了微分流形,上同调,乘积和对偶,基础群,同调理论和同伦理论。包括了面理论,群理论,和纤维丛理论这些大多数拓扑学家想让学拓扑的学生了解的知识点。并且有很多内容很具有启发性,这些内容并不是所有传统的课本中都包含的。通过这本书的阅读也可以提高数学学习能力。尽管这本书具有很强的综合性,但并没有过分去去囊括多余的综合材料,而是这些材料真正地提高了表述的效率和清晰度。

图书封面

图书标签Tags

数学,Topology,几何与拓扑,Mathematics,拓扑学


    拓扑与几何下载



用户评论 (总计25条)

 
 

  •     刚买来,还没看,应该不错
  •     这是我见过的本科以下最好的数学英语教材。
  •     内容广泛但是写的感觉有点乱
  •     以为是新书,封面有一折痕,背面有圆珠笔画了一杠。2008年一月印刷。像换货了,结果只剩一本
  •     在图书馆随便翻过。然后买了。还没看。罪过。
  •     非门勿入,具体还没看
  •     较为详尽但难度不大。,这本书挺不错的
  •     参考书,一直很想了解的一段数学史
  •     趣味性浓厚,张筑生书的序言里提到过。
  •     内容很全面,可惜难度太大
  •     送书的速度和服务的态度我都还挺满意的,看不太懂
  •     给老公买的,当教材买的
  •     一部非常用心的作品。通俗易懂,这样效果更好
  •     讲的很细。,微分拓扑经典教材
  •     帮同学买的教材,俄罗斯经典之作
  •     比较重视直观,作者是微分拓扑学的奠基人
  •     概念讲得很明白,很难读懂
  •     现在收藏着,喜欢!
  •     确实蛮不错的,好书
  •     这书真心不错,书挺喜欢
  •     该书不如宣传的那么好。讲得不够清晰,他觉得比较有参考价值。
  •     这不用说,可里面有几页皱了脏了
  •     拓扑学基础及应用非常喜欢 -- 这本书非常好看,准备以后看完流形和拓扑看
  •     书本质量很好,讲的细
  •     很有看头,但是需要一定的基础
 

自然科学类PDF下载,数学PDF下载。 PPT下载网 

PPT下载网 @ 2017