示性类

图书标准信息

• 作者 [美]米尔纳 著
• 出版社 世界图书出版公司
• 出版时间 2012-06
• 版次 1
• ISBN 9787510005336
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 330页
• 正文语种 英语

【内容简介】

ThetextwhichfollowsisbasedmostlyonlecturesatPrincetonUniversityin1957.Theseniorauthorwishestoapologizeforthedelayinpublication.Thetheoryofcharacteristicclassesbeganintheyear1935withalmostsimultaneousworkbyHASSLERWHITNEYintheUnitedStatesandEDUARDSTIEFELinSwitzerland.StiefeIsthesis，writtenunderthedirectionofHeinzHopf，introducedandstudiedcertain"characteristic"homologyclassesdeterminedbythetangentbundleofasmoothmanifold.Whitney，thenatHarvardUniversity，treatedthecaseofanarbitraryspherebundle.Somewhatlaterheinventedthelanguageofcohomologytheory，hencetheconceptofacharacteristiccohomologyclass，andprovedthebasicproducttheorem.

【目录】

Preface
§1.SmoothManifolds
§2.VectorBundles
§3.ConstructingNewVectorBundlesOutofOld
§4.Stiefel-WhitneyClasses
§5.GrassmannManifoldsandUniversalBundles
§6.ACellStructureforGrassmannManifolds
§7.TheCohomologyRingH*(Gn;Z/2)
§8.ExistenceofStiefel-WhitneyClasses
§9.OrientedBundlesandtheEulerClass
§10.TheThornIsomorphismTheorem
§11.ComputationsinaSmoothManifold
§12.Obstructions
§13.ComplexVectorBundlesandComplexManifolds
§14.ChernClasses
§15.PontrjaginClasses
§16.ChernNumbersandPontrjaginNumbers
§17.TheOrientedCobordismRingΩ*
§18.ThornSpacesandTransversality
§19.MultiplicativeSequencesandtheSignatureTheorem
§20.CombinatorialPontrjaginClasses
Epilogue
AppendixA:SingularHomologyandCohomology
AppendixB:BernoulliNumbers
AppendixC:Connections,Curvature,andCharacteristicClasses.
Bibliography
Index