• 【正版新书】代数拓扑导论
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【正版新书】代数拓扑导论

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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

装帧平装

上书时间2024-05-25

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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
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快递:有多个仓库,中通,极兔等都有合作,不包邮,书本都是出版社,新华书店的库存书,由于部分书籍搬过多个仓库,目前只有80%的书籍有塑封,部分脱落了,书籍保证正版,附件需要私聊确认!
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