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.
Rezensionen / Stimmen
'... a nice introduction to the theory of Frobenius manifolds ...' Zentralblatt fuer Mathematik 'The book under review gives a very detailed analysis of the category of F-manifolds ... the book is clean, rigorous and readable. the researchers in the areas of singularity theory, complex geometry, integrable systems, quantum cohomology, mirror symmetry and sympathetic geometry will find in this book a lot of useful information which has never been given in such detail before.' Proceedings of the Edinburgh Mathematical Society '... 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
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
7 Line drawings, unspecified
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 21 mm
Gewicht
ISBN-13
978-0-521-81296-2 (9780521812962)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Max-Planck-Institut fuer Mathematik in den Naturwissenschaften, Leipzig
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.
