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
装帧平装
上书时间2024-09-12
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图书标准信息
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作者
[美]米尔纳 著
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出版社
世界图书出版公司
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出版时间
2012-06
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版次
1
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ISBN
9787510005336
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定价
39.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
330页
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正文语种
英语
- 【内容简介】
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ThetextwhichfollowsisbasedmostlyonlecturesatPrincetonUniversityin1957.Theseniorauthorwishestoapologizeforthedelayinpublication.Thetheoryofcharacteristicclassesbeganintheyear1935withalmostsimultaneousworkbyHASSLERWHITNEYintheUnitedStatesandEDUARDSTIEFELinSwitzerland.StiefeIsthesis,writtenunderthedirectionofHeinzHopf,introducedandstudiedcertain"characteristic"homologyclassesdeterminedbythetangentbundleofasmoothmanifold.Whitney,thenatHarvardUniversity,treatedthecaseofanarbitraryspherebundle.Somewhatlaterheinventedthelanguageofcohomologytheory,hencetheconceptofacharacteristiccohomologyclass,andprovedthebasicproducttheorem.
- 【目录】
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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
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