代數拓撲導論 [Algebraic Topology:An Introduction]

代數拓撲導論 [Algebraic Topology:An Introduction] 下載 mobi epub pdf 電子書 2024


簡體網頁||繁體網頁
[美] 梅西 著



點擊這裡下載
    


想要找書就要到 圖書大百科
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

發表於2024-12-25

類似圖書 點擊查看全場最低價

圖書介紹

齣版社: 世界圖書齣版公司
ISBN:9787510004421
版次:1
商品編碼:10184569
包裝:平裝
外文名稱:Algebraic Topology:An Introduction
開本:16開
齣版時間:2009-04-01
用紙:膠版紙
頁數:261
正文語種:英語


相關圖書





圖書描述

內容簡介

This textbook is designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as possible. The principal topics treated are 2-dimensional manifolds, the fundamental group, and covering spaces, plus the group theory needed in these topics. The only prerequisites are some group theory, such as that normally contained in an undergraduate algebra course on the junior-senior level, and a one-semester undergraduate course in general topology.
The topics discussed in this book are "standard" in the sense that several well-known textbooks and treatises devote a few sections or a chapter to them. This, I believe, is the first textbook giving a straightforward treatment of these topics, stripped of all unnecessary definitions, terminology, etc., and with numerous examples and exercises, thus making them intelligible to advanced undergraduate students.

內頁插圖

目錄

CHAPTERONETwo-DimensionalManifolds
1 Introduction
2 Definitionandexamplesofn-manifolds
3 Orientablevs.nonorientablemanifolds
4 Examplesofcompact,connected2-manifolds
5 Statementoftheclassificationtheoremforcompactsurfaces
6 Triangulationsofcompactsurfaces
7 ProofofTheorem5.1
8 TheEulercharacteristicofasurface
9 Manifoldswithboundary
10 Theclassificationofcompact,connected2-manifoldswithboundary
11 TheEulercharacteristicofaborderedsurface
12 ModelsofcompactborderedsurfacesinEuclidean3-space
13 Remarksonnoncompactsurfaces

CHAPTERTWOTheFundamentalGroup
1 Introduction
2 Basicnotationandterminology
3 Definitionofthefundamentalgroupofaspace
4 Theeffectofacontinuousmai)pingonthefundamentalgroup
5 Thefundamentalgroupofacircleisinfinitecyclic
6 Application:TheBrouwerfixed-pointtheoremilldimension2
7 Thefundamentalgroupofaproductspace
8 Homotopytypeandhomotopyequivalenceofspaces

CHAPTERTHREEFreeGroupsandFreeProductsofGroups
1 Introduction
2 Theweakproductofabeliangroups
3 Freeabeliangroups
4 Freeproductsofgroups
5 Freegroups
6 Thepresentationofgroupsbygeneratorsandrelations
7 Universalmappingproblems

CHAPTERFOURScifertandVanKampenTheoremontheFundamentalGroupoftheUnionofTwoSpaces.Applic
ations
1 Introduction
2 StatementandproofofthetheoremofSeifertandVanKampen
3 FirstapplicationofTheorem2.1
4 SecondapplicationofTheorem2.1
5 Structureofthefundamentalgroupofacompactsurface
6 Applicationtoknottheory

CHAPTERFIVECoveringSpaces
1 Introduction
2 Definitionandsomeexamplesofcoveringspaces
3 Liftingofpathstoacoveringspace
4 Thefundamentalgroupofacoveringspace
5 Liftingofarbitrarymapstoacoveringspace
6 Homomorphismsandautomorphismsofcoveringspaces
7 Theactionofthegroupπ(X,x)onthesetp-(x)
8 Regularcoveringspacesandquotientspaces
9 Application:TheBorsuk-Ulamtheoremforthe2-sphere
10 Theexistencetheoremforcoveringspaces
11 Theinducedcoveringspaceoverasubspace
12 Pointsettopologyofcoveringspaces

CHAPTERSIXTheFundamentalGroupandCoveringSpacesofaGraph.ApplicationstoGroupTheory
1 Introduction
2 Definitionandexamples
3 Basicpropertiesofgraphs
4 Trees
5 Thefundamentalgroupofagraph
6 TheEulercharacteristicofafinitegraph
7 Coveringspacesofagraph
8 Generatorsforasubgroupoffreegroup

CHAPTERSEVENTheFundamentalGroupofHigherDimensionalSpaces
1 Introduction
2 Adjunctionof2-cellstoaspace
3 Adjunctionofhigherdimensionalcellstoaspace
4 CW-complexes
5 TheKuroshsubgrouptheorem
6 GrushkosTheorem

CHAPTEREIGHTEpilogue
APPENDIXATheQuotientSpaceorIdentificationSpaceTopology
1 Definitionsandbasicproperties
2 Ageneralizationofthequotientspacetopology
3 Quotientspacesandproductspaces
4 Subspaceofaquotientspacevs.quotientspaceofasubspace
5 ConditionsforaquotientspacetobeaHausdorffspace

APPENDIXBPermutationGroupsorTransformationGroups
1 Basicdefinitions
2 HomogeneousG-spaces
Index

前言/序言

  This textbook iS designed to introduce advanced undergraduate or beginning graduate students to algebraic topology as painlessly as pos- sible.The principal topics treated are 2.dimcnsional manifolds.the fundamental group,and covering spaces,plus the group theory needed in these topics.The only prerequisites are some group theory,such as that normally centained jn an undergraduate algebra course on the junior-senior level,and a one·semester undergraduate course in general topology.
  The topics discussed in this book are“standard”in the sense that several well-known textbooks and treatises devote a fey.r sections or a chapter to them.This。I believe,iS the first textbook giving a straight- forward treatment of these topics。stripped of all unnecessary definitions, terminology,etc.,and with numerous examples and exercises,thus making them intelligible to advanced undergraduate students.
  The SUbject matter i8 used in several branches of mathematics other than algebraic topology,such as differential geometry,the theory of Lie groups,the theory of Riemann surfaces。or knot theory.In the develop- merit of the theory,there is a nice interplay between algebra and topology which causes each to reinfoFee interpretations of the other.Such an interplay between different topics of mathematics breaks down the often artificial subdivision of mathematics into difierent“branches”and emphasizes the essential unity of all mathematics.

代數拓撲導論 [Algebraic Topology:An Introduction] 下載 mobi epub pdf txt 電子書 格式

代數拓撲導論 [Algebraic Topology:An Introduction] mobi 下載 pdf 下載 pub 下載 txt 電子書 下載 2024

代數拓撲導論 [Algebraic Topology:An Introduction] 下載 mobi pdf epub txt 電子書 格式 2024

代數拓撲導論 [Algebraic Topology:An Introduction] 下載 mobi epub pdf 電子書
想要找書就要到 圖書大百科
立刻按 ctrl+D收藏本頁
你會得到大驚喜!!

用戶評價

評分

娃爸買的……學幾何的

評分

這個可以作為代數拓撲的入門書

評分

很好…………

評分

很好…………

評分

評分

給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆豆給豆

評分

金典書籍

評分

可以。。。。。。。。。。。。。。。

評分

娃爸買的……學幾何的

類似圖書 點擊查看全場最低價

代數拓撲導論 [Algebraic Topology:An Introduction] mobi epub pdf txt 電子書 格式下載 2024


分享鏈接




相關圖書


本站所有內容均為互聯網搜索引擎提供的公開搜索信息,本站不存儲任何數據與內容,任何內容與數據均與本站無關,如有需要請聯繫相關搜索引擎包括但不限於百度google,bing,sogou

友情鏈接

© 2024 book.qciss.net All Rights Reserved. 圖書大百科 版權所有