Frobenius Manifolds and Moduli Spaces for Singularities

This book presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications.

Claus Hertling (Author)

9780521812962, Cambridge University Press

Hardback, published 25 July 2002

282 pages, 7 b/w illus.
23.6 x 15.5 x 1.9 cm, 0.59 kg

'… one can say this book is a must for workers in the field of singularity theory.' Duco van Straten, Department of Mathematics, University of Mainz

The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with 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.

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. Connections on the punctured plane
8. Meromorphic connections
9. Frobenius manifolds ad second structure connections
10. Gauss-Manin connections for hypersurface singularities
11. Frobenius manifolds for hypersurface singularities
12. ???-constant stratum
13. Moduli spaces for singularities
14. Variance of the spectral numbers.

Subject Areas: Topology [PBP], Geometry [PBM], Calculus & mathematical analysis [PBK]