自旋几何

图书标准信息

• 作者 [美]劳森 著
• 出版社 世界图书出版公司
• 出版时间 2011-01
• 版次 1
• ISBN 9787510029639
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 427页
• 原版书名 Spin Geometry

【内容简介】

inthelate1920stherelentlessmarchofideasanddiscoverieshadcarriedphysicstoagenerallyacceptedrelativistictheoryoftheelectron.thephysicistp.a.m.dirac，however，wasdissatisfiedwiththeprevailingideasand，somewhatinisolation，soughtforabetterformulation.by1928hesucceededinfindingatheorywhichaccordedwithhisownideasandalsofitmostoftheestablishedprinciplesofthetime.ultimatelythistheoryprovedtobeoneofthegreatintellectualachievementsoftheperiod.itwasparticularlyremarkablefortheinternalbeautyofitsmathematicalstructurewhichnotonlyclarifiedmuchpreviouslymysteriousphenomenabutalsopredictedinacompellingwaytheexistenceofanelectron-likeparticleofnegativeenergy.indeedsuchparticlesweresubsequentlyfoundtoexistandourunderstandingofnaturewastransformed.
becauseofitscompellingbeautyandphysicalsignificanceitisperhapsnotsurprisingthattheideasattheheartofdiracstheoryhavealsobeendiscoveredtoplayaroleofgreatimportanceinmodernmathematics，particularlyintheinterrelationsbetweentopology，geometryandanalysis.agreatpartofthisnewunderstandingcomesfromtheworkofm.atiyahandi.singer.itistheirworkanditsimplicationswhichformthefocusofthisbook.

【目录】

preface
acknowledgments
introduction
chapterⅰcliffordalgebras，spingroupsandtheir
representations
1.cliffordalgebras
2.thegroupspinandspin
3.thealgebrascln，andclr，s
4.theclassification
5.representations
6.liealgebrastructures
7.somedirectapplicationstogeometry
8.somefurtherapplicationstothetheoryofliegroups
9.k-theoryandtheatiyah-bott-shapiroconstruction
10.kr-theoryandthe（1，1）-periodicitytheorem
chapterⅱspingeometryandthediracoperators
1.spinstructuresonvectorbundles
2.spinmanifoldsandspincobordism
3.cliffordandspinorbundles
.4.connectionsonspinorbundles
5.thediracoperators
6.thefundamentalellipticoperators
7.clk-lineardiracoperators
8.vanishingtheoremsandsomeapplications
chapterⅲindextheorems
1.differentialoperators
2.sobolevspacesandsobolevtheorems
3.pseudodifferentialoperators
4.ellipticoperatorsandparametrices
5.fundamentalresultsforellipticoperators
6.theheatkernelandtheindex
7.thetopologicalinvarianceoftheindex
8.theindexofafamilyofellipticoperators
9.theg-index
10.thecliffordindex
11.multiplicativesequencesandthecherncharacter
12.thomisomorphismsandthecherncharacterdefect
13.theatiyah-singerindextheorem
14.fixed-pointformulasforellipticoperators
15.theindextheoremforfamilies
16.familiesofrealoperatorsandtheclk-indextheorem
17.remarksonheatandsupersymmetry
chapterⅳapplicationsingeometryandtopology
1.lntegralitytheorems
2.immersionsofmanifoldsandthevectorfieldproblem
3.groupactionsonmanifolds
4.compactmanifoldsofpositivescalarcurvature
5.positivescalarcurvatureandthefundamentalgroup
6.completemanifoldsofpositivescalarcurvature
7.thetopologyofthespaceofpositivescalarcurvaturemetrics
8.cliffordmultiplicationandkiihlermanifolds
9.purespinors，complexstructures，andtwistors
10.reducedholonomyandcalibrations
11.spinorcohomologyandcomplexmanifoldswithvanishingfirstchernclass
12.thepositivemassconjectureingeneralrelativity
appendixaprincipalg-bundles
appendixbclassifyingspacesandcharacteristicclasses
appendixcorientationclassesandthomisomorphismsink-theory
appendixdspine-manifolds
bibliography
index
notationindex