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Frobenius Manifolds and Moduli Spaces for Singularities : Cambridge Tracts in Mathematics - Claus Hertling

Frobenius Manifolds and Moduli Spaces for Singularities

Cambridge Tracts in Mathematics


Published: 27th February 2014
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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.

'... a nice introduction to the theory of Frobenius manifolds ...' Zentralblatt fur 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

Multiplication on the Tangent Bundle
Introduction to part 1
Definition and first properties of F-manifolds
Massive F-manifolds and Lagrange maps
Discriminants and modality of F-manifolds
Singularities and Coxeter groups
Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities
Introduction to part 2
Connections on the punctured plane
Meromorphic connections
Frobenius manifolds ad second structure connections
Gauss-Manin connections for hypersurface singularities
Frobenius manifolds for hypersurface singularities
âê´Î¼Ïà-constant stratum
Moduli spaces for singularities
Variance of the spectral numbers
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521812962
ISBN-10: 0521812968
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 282
Published: 27th February 2014
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.9
Weight (kg): 0.59