标题： 二维拓扑场论的几何学 显示英文标题

标题： Geometry of 2d topological field theories

摘要： 这些讲义致力于研究描述二维拓扑场论模空间几何的结合性方程理论。 引言。 第1讲。 WDVV 方程与 Frobenius 流形。 {附录 A.} WDVV 的多项式解。 {附录 B.} WDVV 的对称性。 Twisted Frobenius 流形。 {附录 C.} WDVV 与 Chazy 方程。 具有射影结构的曲线上的仿射联络。 第2讲。 拓扑共形场论及其模。 第3讲。 等单色形变形空间作为 Frobenius 流形。 {附录 D.} 度量平坦偶的几何。 {附录E} WDVV 与 Painlevé-VI。 {附录 F.} 等单色形变形方程解的分支与编织群。 {附录 G。} Frobenius 流形的单值群。 {附录 H。} 与Frobenius流形相关的广义超几何方程及其单值群。 {附录 I.} 确定Frobenius流形的超势。 第4讲。 Coxeter群轨道空间上的Frobenius结构。 {附录 J.} 扩展的复数晶体群和扭曲的Frobenius流形。 第5讲。 Hurwitz空间的微分几何。 第6讲。 Frobenius流形与可积层次。 与拓扑引力耦合。 显示英文摘要

摘要： These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial solutions of WDVV. {Appendix B.} Symmetriies of WDVV. Twisted Frobenius manifolds. {Appendix C.} WDVV and Chazy equation. Affine connections on curves with projective structure. Lecture 2. Topological conformal field theories and their moduli. Lecture 3. Spaces of isomonodromy deformations as Frobenius manifolds. {Appendix D.} Geometry of flat pencils of metrics. {Appendix E.} WDVV and Painlev\'e-VI. {Appendix F.} Branching of solutions of the equations of isomonodromic deformations and braid group. {Appendix G.} Monodromy group of a Frobenius manifold. {Appendix H.} Generalized hypergeometric equation associated to a Frobenius manifold and its monodromy. {Appendix I.} Determination of a superpotential of a Frobenius manifold. Lecture 4. Frobenius structure on the space of orbits of a Coxeter group. {Appendix J.} Extended complex crystallographic groups and twisted Frobenius manifolds. Lecture 5. Differential geometry of Hurwitz spaces. Lecture 6. Frobenius manifolds and integrable hierarchies. Coupling to topological gravity.