Frobenius Manifolds and Moduli Spaces for Singularities

ISBN-13: 9780521812962 / Angielski / Twarda / 2002 / 282 str.

Claus Hertling; B. Bollobas; W. Fulton

Opis

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.

Recenzje

'… 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

Spis treści

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. ∴μυ-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.