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

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

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


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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

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



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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] epub pdf mobi txt 電子書 下載 2024

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

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

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