出版社：世界图书出版公司北京公司
年代：2009
定价：29.0
本书是作者以在美国耶鲁大学任教多年的讲义为基础写成的。它论述了代数拓扑学的基础理论：二维流形、基本群、覆盖空间等，并强调通过映射问题；书中还给出了群论中几个有名定理的证明。
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
4Theeffectofacontinuousmappingonthefundamentalgroup
5Thefundamentalgroupofacircleisinfinitecyelic
6Application:TheBrouwerfixed-pointtheoremindimension2
7Thefundamentalgroupofaproductspace
8Homotopytypeandhomotopyequivalenceofspaces
CHAPTERTHREEFreeGroupsandFreeProductsofGroups
1Introduction
2Theweakproductofabeliangroups
3Freeabeliangroups
4Freeproductsofgroups
5Freegroups
6Thepresentationofgroupsbygeneratorsandrelations
7Universalmappingproblems
CHAPTERFOURSeifertandVanKampenTheoremontheFundamentalGroupoftheUnionofTwoSpaces.Applications
1Introduction
2StatementandproofofthetheoremofSeifertandVanKampen
3FirstapplicationofTheorem2.1
4SecondapplicationofTheorem2.1
5Structureofthefundamentalgroupofacompactsurface
6Applicationtoknottheory
CHAPTERFIVECoveringSpaces
1Introduction
2Definitionandsomeexamplesofcoveringspaces
3Liftingofpathstoacoveringspace
4Thefundamentalgroupofacoveringspace
5Liftingofarbitrarymapstoacoveringspace
6Homomorphismsandautomorphismsofcoveringspaces
7Theactionofthegroupπ(X,x)onthesetp-τ(x)
8Regularcoveringspacesandquotientspaces
9Application:TheBorsuk-Ulamtheoremforthe2-sphere
10Theexistencetheoremforcoveringspaces
llTheinducedcoveringspaceoverasubspace
12Pointsettopologyofcoveringspaces
CHAPTERSIXTheFundamentalGroupandCoveringSpacesofaGraph.
ApplicationstoGroupTheory
1Introduction
2Definitionandexamples
3Basicpropertiesofgraphs
4Trees
5Thefundamentalgroupofagraph
6TheEulercharacteristicofafinitegraph
7Coveringspacesofagraph
8Generatorsforasubgroupoffreegroup
CHAPTERSEVENTheFundamentalGroupofHigherDimensionalSpaces
1Introduction
2Adjunctionof2-cellstoaspace
3Adjunctionofhigherdimensionalcellstoaspace
4CW-complexes
5TheKuroshsubgrouptheorem
6GrushkosTheorem
CHAPTEREIGHT
Epilogue
APPENDIXA
TheQuotientSpaceor|dentificationSpaceTopology
1Definitionsandbasicproperties
2Ageneralizationofthequotientspacetopology
3Quotientspacesandproductspaces
4Subspaeeofaquotientspacevs.quotientspaceofasubspace
5ConditionsforaquotientspacetobeaHausdorffspace
APPENDIXB
PermutationGroupsorTransformationGroups
1Basicdefinitions
2HomogeneousG-spaces
Index
Thistextbookisdesignedtointroduceadvancedundergraduateorbeginninggraduatestudentstoalgebraictopologyaspainlesslyaspossible.Theprincipaltopicstreatedare2-dimensionalmanifolds,thefundamentalgroup,andcoveringspaces,plusthegrouptheoryneededinthesetopics.Theonlyprerequisitesaresomegrouptheory,suchasthatnormallycontainedinanundergraduatealgebracourseonthejunior-seniorlevel,andaone-semesterundergraduatecourseingeneraltopology.
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| 出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
| 版次 | 1版 | 印次 | 1 |
| 定价(元) | 29.0 | 语种 | 英文 |
| 尺寸 | 14 | 装帧 | 平装 |
| 页数 | 印数 | 1000 | |
代数拓扑导论是世界图书出版公司北京公司于2009.04出版的中图分类号为 O189.2 的主题关于 代数拓扑－英文 的书籍。