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[美] 科恩 (Ralph L.Cohen)、[美] 科恩 / 科学出版社 / 2011-06 / 精装
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弦拓扑与环同调
《弦拓扑与环同调(影印版)》的两部分分别介绍StringTopology与CyclicHomology,都是十几年来代数拓扑学中的新发展,freeloopspace都在其中起着中心作用。属于“反映学术前沿进展的优秀学术著作”这一类。比较专门,对象是研究生。
ForewordINotesonStringTopologyRalphL.CohenandAlexanderA.VronovIntroductionlIntersectiontheoryinloopspaces1.1Intersectionsincompactmanifolds1.2TheChas-Sullivanloopproduct1.3TheBVstructureandthestringbracket1.4Astablehomotopypointofview1.5RelationtoHochschildcohomology2Thecactioperad2.1PROPsandoperads2.1.1PROP’S2.1.2AlgebrasoveraPROP2.1.3Operads2.1.4Algebrasoveranoperad2.1.5Operadsviageneratorsandrelations2.2Thecactioperad2.3Thecactiactionontheloopspace2.3.1ActionviacOrrespOndences2.3.2TheBVstructure3Stringtopologyasfieldtheory3.1Fieldtheories3.1.1TopologicalFieldTheories3.1.2(Topological)ConformalFieldTheories3.1.3Examples3.1.4MotivicTCFTs3.2Generalizedstringtopologyoperations3.3Open-closedstringtopology4AMorsetheoreticviewpoint4.1Cylindricalgradientgraphflows4.2CylindricalholomorphiccurvesinT*M5Brahetopology5.1Thehigher-dimensionalcactioperad5.2Thecactiactiononthespherespace5.3Thealgebraicstructureonhomology5.4SpherespacesandHochschildhomologyBibliographyIIAnAlgebraicModelforMod2TopologicalCyclicHomologyKathrynHe88Preface1Preliminaries1.1Elementarydefinitions,terminologyandnotation1.2Thecanonical,enrichedAdams-Hiltonmodel1.2.1Twistingcochains1.2.2Stronglyhomotopycoalgebraandcomodulemaps1.2.3ThecanonicalAdams-Hiltonmodel1.3Noncommutativealgebraicmodelsoffibersquares2Freeloopspaces2.1Asimplicialmodelforthefreeloopspace2.1.1Thegeneralmodel2.1.2Choosingthefreeloopmodelfunctorially2.2Themultiplicativefreeloopspacemodel2.2.1Thediagonalmap2.2.2Thepathfibration2.2.3Thefreeloopspacemodel2.3Thefreeloopmodelfortopologicalspaces2.4Linearizationofthefreeloopmodel3Homotopyorbitspaces3.1Aspecialfamilyofprimitives3.2AusefulresolutionofCU*ES13.3ModelingS1homotopyorbits3.4Thecaseofthefreeloopspace……
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