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《代数拓扑导论》是由世界图书出版公司出版的。

内容简介

《代数拓扑导论》讲述了：Thistextbookisdesignedtointroduceadvancedundergraduateorbeginninggraduatestudentstoalgebraictopologyaspainlesslyaspossible.Theprincipaltopicstreatedare2-dimensionalmanifolds,thefundamentalgroup,andcoveringspaces,plusthegrouptheoryneededinthesetopics.Theonlyprerequisitesaresomegrouptheory,suchasthatnormallycontainedinanundergraduatealgebracourseonthejunior-seniorlevel,andaone-semesterundergraduatecourseingeneraltopology.
Thetopicsdiscussedinthisbookare"standard"inthesensethatseveralwell-knowntextbooksandtreatisesdevoteafewsectionsorachaptertothem.This,Ibelieve,isthefirsttextbookgivingastraightforwardtreatmentofthesetopics,strippedofallunnecessarydefinitions,terminology,etc.,andwithnumerousexamplesandexercises,thusmakingthemintelligibletoadvancedundergraduatestudents.

作者简介

作者：(美国)梅西(Massey.W.S.)

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
6Grushko'sTheorem

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

APPENDIXBPermutationGroupsorTransformationGroups
1Basicdefinitions
2HomogeneousG-spaces
Index

代数拓扑导论

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