Frobenius manifolds and moduli spaces for singularities / Claus Hertling.

Format:

Book

Author/Creator:

Hertling, Claus, author.

Series:

Cambridge tracts in mathematics ; 151.

Cambridge tracts in mathematics ; 151

Language:

English

Subjects (All):

Singularities (Mathematics).

Frobenius algebras.

Moduli theory.

Physical Description:

1 online resource (ix, 270 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Frobenius Manifolds & Moduli Spaces for Singularities

Place of Publication:

Cambridge : Cambridge University Press, 2002.

Language Note:

English

Summary:

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.

Contents:

Multiplication on the tangent bundle

First examples

Fast track through the results

Definition and first properties of F-manifolds

Finite-dimensional algebras

Vector bundles with multiplication

Definition of F-manifolds

Decomposition of F-manifolds and examples

F-manifolds and potentiality

Massive F-manifolds and Lagrange maps

Lagrange property of massive F-manifolds

Existence of Euler fields

Lyashko-Looijenga maps and graphs of Lagrange maps

Miniversal Lagrange maps and F-manifolds

Lyashko-Looijenga map of an F-manifold

Discriminants and modality of F-manifolds

Discriminant of an F-manifold

2-dimensional F-manifolds

Logarithmic vector fields

Isomorphisms and modality of germs of F-manifolds

Analytic spectrum embedded differently

Singularities and Coxeter groups

Hypersurface singularities

Boundary singularities

Coxeter groups and F-manifolds

Coxeter groups and Frobenius manifolds

3-dimensional and other F-manifolds

Frobenius manifolds, Gauss-Manin connections, and moduli spaces for hypersurface singularities

Construction of Frobenius manifolds for singularities

Moduli spaces and other applications

Connections over the punctured plane

Flat vector bundles on the punctured plane

Lattices

Saturated lattices

Riemann-Hilbert-Birkhoff problem

Spectral numbers globally

Meromorphic connections

Logarithmic vector fields and differential forms

Logarithmic pole along a smooth divisor

Logarithmic pole along any divisor.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 260-267) and index.

ISBN:

1-107-12564-2

1-280-43401-5

0-511-04541-7

9786610434015

0-511-14774-0

0-511-17741-0

0-511-30500-1

0-511-54310-7

OCLC:

559254871