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Frobenius Manifolds and Moduli Spaces for Singularities: Cambridge Tracts in Mathematics, cartea 151

Autor Claus Hertling
en Limba Engleză Hardback – 24 iul 2002
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.
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Specificații

ISBN-13: 9780521812962
ISBN-10: 0521812968
Pagini: 282
Ilustrații: 7 b/w illus.
Dimensiuni: 155 x 236 x 19 mm
Greutate: 0.51 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

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.

Recenzii

'… a nice introduction to the theory of Frobenius manifolds …' Zentralblatt für 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

Descriere

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