弦拓撲與環同調（簡體書）

《弦拓撲與環同調(影印版)》的兩部分分別介紹StringTopology與CyclicHomology，都是十幾年來代數拓撲學中的新發展，freeloopspace都在其中起著中心作用。屬于“反映學術前沿進展的優秀學術著作”這一類。比較專門，對象是研究生。

作者：（美國）科恩（Ralph L.Cohen） （美國）Kathryn Hess （美國）Alexander A.Voronov

《弦拓撲與環同調(影印版)》：This book explores string topology, Hochschild and cyclic homology,assembling material from a wide scattering of scholarly sources ina single practical volume. The first part offers a thorough and elegantexposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clearconstruction of an algebraic model for computing topological cyclichomology.

ForewordⅠ Notes on String TopologyRalph L.Cohen and Alexander A.VronovIntroductionl Intersection theory in loop spaces1.1 Intersections in compact manifolds1.2 The Chas-Sullivan loop product1.3 The BV structure and the string bracket1.4 A stable homotopy point of view1.5　Relation to Hochschild cohomology2 The cacti operad2.1 PROPs and operads2.1.1　PROP’S2.1.2 Algebras over a PROP2.1.3　Operads2.1.4 Algebras over an operad2.1.5 Operads via generators and relations2.2 The cacti operad2.3 The cacti action on the loop space2.3.1　Action via cOrrespOndences2.3.2　The BV structure3 String topology as field theory3.1 Field theories3.1.1 Topological Field Theories3.1.2(Topological)Conformal Field Theories3.1.3　Examples3.1.4 Motivic TCFTs3.2 Generalized string topology operations3.3 Open-closed string topology4 A Morse theoretic viewpoint4.1 Cylindrical gradient graph flows4.2 Cylindrical holomorphic curves in T*M5 Brahe topology5.1 The higher-dimensional cacti operad5.2 The cacti action on the sphere space5.3 The algebraic structure on homology5.4 Sphere spaces and Hochschild homologyBibliographyⅡ An Algebraic Model for Mod 2 Topological Cyclic HomologyKathryn He88Preface1 Preliminaries1.1　Elementary definitions，terminology and notation1.2 The canonical，enriched Adams-Hilton model1.2.1 Twisting cochains1.2.2 Strongly homotopy coalgebra and comodule maps1.2.3 The canonical Adams-Hilton model1.3 Noncommutative algebraic models of fiber squares2 Free loop spaces2.1 A simplicial model for the free loop space2.1.1　The general model2.1.2　Choosing the free loop model functorially2.2 The multiplicative free loop space model2.2.1　The diagonal map2.2.2　The path fibration2.2.3　The free loop space model2.3 The free loop model for topological spaces2.4 Linearization of the free loop model3 Homotopy orbit spaces3.1 A special family of primitives3.2 A useful resolution of CU*ES13.3 Modeling S1 homotopy orbits3.4 The case of the free loop space4 A model for mod 2 topological cyclic homology 4.1 The pth-power map 4.2 Topological cyclic homology Bibliography

Thebiholomorphic maps are part of the data, which in particular means that choosinga different biholomorphic map for the same hole is likely to change the point inthe moduli space. The more precise nonoverlapping condition is that the closeddisks in the inputs do not intersect pairwise and the closed disks in the outputs donot intersect pairwise, however, an input and an output disk may have commonboundary, but are still not allowed to intersect at an interior point. This techni-cality brings in the identity morphisms to the PROP, but does not create singularRiemann surfaces by composition. The composition of morphisms in this PROPis given by sewing the Riemann surfaces along the boundaries, using the equationzw = 1 in the holomorphic parameters coming from the standard one on the unitdisk. The tensor product of morphisms is the disjoint union. This PROP plays acrucial role in Conformal Field Theory, as we will see now.