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Other titles in the Cambridge Tracts in Mathematics series:
Cambridge Tracts in Mathematics #151: Frobenius Manifolds and Moduli Spaces for Singularitiesby Claus Hertling
Synopses & Reviews
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.
Book News Annotation:
Addresses the relations between Frobenius manifolds and singularity theory, in two parts. The first section studies F-manifolds, discriminants, and Lagrange maps and their singularities, with some of Givental's work used as an application to prove a conjecture of Dubrovin about Frobenius manifolds and Coxeter groups. The second part takes up the construction of Frobenius manifolds in singularity theory, providing an elementary but detailed explanation, with results developed and cited. Suitable for readers with an understanding of the basic concepts of complex analytic geometry, including coherent sheaves and flatness.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
The author presents the theory of Frobenius manifolds, as well as all the necessary tools and several applications. Readers will find here a careful study of this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students wishing to work in this area.
The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. The author presents a simplified exposition of the theory as well as 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.
Theory of Frobenius manifolds, as well as all the necessary tools and several applications.
Table of Contents
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. \mu-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.
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