Frobenius Manifolds and Moduli Spaces for Singularities [Hardcover]

This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. The author presents a simplified exposition of the theory as well as all the necessary tools and several applications. Readers will find here, a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. The author presents a simplified exposition of the theory as well as all the necessary tools and several applications. Readers will find here, a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.For those working in singularity theory or other areas of complex geometry, this volume will open the door to the study of Frobenius manifolds. In the first part Hertling explains the theory of manifolds with a multiplication on the tangent bundle. He then presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will benefit from this careful and sound study of the fundamental structures and results in this exciting branch of mathematics.Part I. Multiplication on the Tangent Bundle: 1. Introduction to part 1; 2. Definition and first properties of F-manifolds; 3. Massive F-manifolds and Lagrange maps; 4. Discriminants and modality of F-manifolds; 5. Singularities and Coxeter groups; Part II. Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities: 6. Introduction to part 2; 7. Cl“+