可微流形和李群基础

图书标准信息

• 作者 Frank W.Warner 编
• 出版社 世界图书出版公司
• 出版时间 2004-04
• 版次 1
• ISBN 9787506266055
• 定价 39.00元
• 装帧 平装
• 开本 其他
• 纸张 胶版纸
• 页数 272页

【内容简介】

Thisbookprovidesthenecessaryfoundationforstudentsinterestedinanyofthediverseareasofmathematicswhichrequirethenotionofadifferentiablemanifold.Itisdesignedasabeginninggraduate-leveltextbookandpresumesagoodundergraduatetraininginalgebraandanalysisplussomeknowledgeofpointsettopology,coveringspaces,andthefundamentalgroup.Itisalsointendedforuseasareferencebooksinceitincludesanumberofitemswhicharedifficulttoferretoutoftheliterature,inparticular,thecompleteandself-containedproofsofthefundamentaltheoremsofHodgeanddeRham.

【目录】

1MANIFOLDS
Preliminaries
DifferentiableManifolds
TheSecondAxiomofCountability
TangentVectorsandDifferentials
Submanifolds，Diffeomorphisms，andtheInverseFunctionTheorem
ImplicitFunctionTheorems
VectorFields
DistributionsandtheFrobeniusTheorem
Exercises

2TENSORSANDDIFFERENTIALFORMS
TensorandExteriorAlgebras
TensorFieldsandDifferentialForms
TheLieDerivative
DifferentialIdeals
Exercises

3IEGROUPS
LieGroupsandTheirLieAlgebras
Homomorphisms
LieSubgroups
Coverings
SimplyConnectedLieGroups
ExponentialMap
ContinuousHomomorphisms
ClosedSubgroups
TheAdjointRepresentation
AutomorphismsandDerivationsofBilinearOperationsandForms
HomgeneousManifolds
Exercises
4INTEGRATIONONMANIFOLDS
5SHEAVES,COHOMOLGY,ANDTHEDERHAMTHEOREM
6THEHODGETHEOREM
BIBLIOGRAPHY
SUPPLEMENTTOBIBLIOGRAPHY
INDEXOFNOTATION
INDEX