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[美] 梅西 著
出版社: 世界图书出版公司 ISBN:9787510004421 版次:1 商品编码:10184569 包装:平装 外文名称:Algebraic Topology:An Introduction 开本:16开 出版时间:2009-04-01 用纸:胶版纸 页数:261 正文语种:英语
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.
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
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.
代数拓扑导论 [Algebraic Topology:An Introduction] 电子书 下载 mobi epub pdf txt
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代数拓扑导论 [Algebraic Topology:An Introduction] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
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[美] 梅西 著
出版社: 世界图书出版公司 ISBN:9787510004421 版次:1 商品编码:10184569 包装:平装 外文名称:Algebraic Topology:An Introduction 开本:16开 出版时间:2009-04-01 用纸:胶版纸 页数:261 正文语种:英语
内容简介
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.
内页插图
目录
CHAPTERONETwo-DimensionalManifolds1 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.
代数拓扑导论 [Algebraic Topology:An Introduction] 电子书 下载 mobi epub pdf txt
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