变换群与曲线模空间（英文版）

图书标准信息

• 作者 季理真、丘成桐 著
• 出版社 高等教育出版社
• 出版时间 2010-06
• 版次 1
• ISBN 9787040298420
• 定价 69.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 298页
• 字数 480千字
• 正文语种 英语

【内容简介】

Transformationgroupshaveplayedafundamentalroleinmanyareasofmathematicssuchasdifferentialgeometry,geometrictopology,algebraictopology,algebraicgeometry,numbertheory.Oreofthebasicreasonsfortheirimportanceisthatsymmetriesaredescribedbygroups(orrathergroupactions).Quotientsofsmoothmanifoldsbygroupactionsareusuallynotsmoothmanifolds.Ontheotherhand,iftheactionsofthegroupsareproper,thenthequotientsareorbifolds.AnimportantexampleisgivenbytheactionofthemappingclassgroupsontheTeichmullerspaces,andthequotientsgivethemodulispacesofRiemannsurfaces(oralgebraiccurves)andareorbifolds.
Thisbookconsistsofexpandedlecture'notesoftwosummerschoolsTransformationGroupsandOrbifoldsandGeometryofTeichmullerSpacesandModuliSpacesofCurvesin2008andwillbeavaluablesourceforpeopletolearntransformationgroups,orbifolds,Teichmullerspaces,mappingclassgroups,modulisoacesofcurvesandrelatedtopics.

【目录】

LecturesonOrbifoldsandGroupCohomology
AlejandroAdemandMicheleKlaus
1Introduction
2Classicalorbifolds
3Examplesoforbifolds
4Orbifoldsandmanifolds
5Orbifoldsandgroupoids
6TheorbifoldEulercharacteristicandK-theory
7StringyproductsinK-theory
8Twistedversion
References
LecturesontheMappingClassGroupofaSurface
ThomasKwok-KeungAu,FengLuoandTianYang
Introduction
1Mappingclassgroup
2Dehn-LickorishTheorem
3Hyperbolicplaneandhyperbolicsurfaces
4Quasi-isometryandlargescalegeometry
5Dehn-NielsenTheorem
References
LecturesonOrbifoldsandReflectionGroups
MichaelW.Davis
1Transformationgroupsandorbifolds
22-dimensionalorbifolds
3Reflectiongroups
43-dimensionalhyperbolicreflectiongroups
5Asphericalorbifolds
References
LecturesonModuliSpacesofEllipticCurves
RichardHain
1Introductiontoellipticcurvesandthemoduliproblem
2Familiesofellipticcurvesandtheuniversalcurve
3TheorbifoldM1,1
4Theorbifold■1,1andmodularforms
5Cubiccurvesandtheuniversalcurve■→■1,1
6ThePicardgroupsofM1,1and■1,1
7Thealgebraictopologyof■1,1
8Concludingremarks
AppendixABackgroundonRiemannsurfaces
AppendixBAverybriefintroductiontostacks
References
AnInvitationtotheLocalStructuresofModuliofGenusOneStableMaps
YiHU
1Introduction
2Thestructuresofthedirectimagesheaf
3Extensionsofsectionsonthecentralfiber
References
LecturesontheELSVFormula
Chiu-ChuMelissaLiu
1Introduction
2HurwitznumbersandHodgeintegrals
3Equivariantcohomologyandlocalization
4ProofoftheELSVformulabyvirtuallocalization
References
FormulaeofOne-partitionandTwo-partitionHodgeIntegrals
Chiu-ChuMelissaLiu
1Introduction
2TheMarino-Vafaformulaofone-partitionHodgeintegrals
3ApplicationsoftheMarifio-Vafaformula
4ThreeapproachestotheMarino-Vafaformula
5ProofofProposition4.3
6Generalizationtothetwo-partitioncase
References
LecturesonElementsofTransformationGroupsandOrbifolds
ZhiLu
1TopologicalgroupsandLiegroups
2G-actions(ortransformationgroups)ontopologicalspaces
3Orbifolds
4Homogeneousspacesandorbittypes
5Twistedproductandslice
6Equivariantcohomology
7Davis-Januszkiewicztheory
References
TheActionoftheMappingClassGrouponRepresentationVarieties
RichardA.Wentworth
1Introduction
2ActionofOut(π)onrepresentationvarieties
3Actiononthecohomologyofthespaceoffiatunitaryconnections
4ActiononthecohomologyoftheSL(2,C)charactervariety
References