代数拓扑导论

图书标准信息

• 作者 [美]梅西 著
• 出版社 世界图书出版公司
• 出版时间 2009-04
• 版次 1
• ISBN 9787510004421
• 定价 29.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 261页
• 正文语种 英语

【内容简介】

Thistextbookisdesignedtointroduceadvancedundergraduateorbeginninggraduatestudentstoalgebraictopologyaspainlesslyaspossible.Theprincipaltopicstreatedare2-dimensionalmanifolds，thefundamentalgroup，andcoveringspaces，plusthegrouptheoryneededinthesetopics.Theonlyprerequisitesaresomegrouptheory，suchasthatnormallycontainedinanundergraduatealgebracourseonthejunior-seniorlevel，andaone-semesterundergraduatecourseingeneraltopology.
Thetopicsdiscussedinthisbookare"standard"inthesensethatseveralwell-knowntextbooksandtreatisesdevoteafewsectionsorachaptertothem.This，Ibelieve，isthefirsttextbookgivingastraightforwardtreatmentofthesetopics，strippedofallunnecessarydefinitions，terminology，etc.，andwithnumerousexamplesandexercises，thusmakingthemintelligibletoadvancedundergraduatestudents.

【目录】

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

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

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

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

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

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

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

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

APPENDIXBPermutationGroupsorTransformationGroups
1Basicdefinitions
2HomogeneousG-spaces
Index