Franklin

Frobenius manifolds and moduli spaces for singularities / Claus Hertling. [electronic resource]

Author/Creator:
Hertling, Claus, author.
Publication:
Cambridge : Cambridge University Press, 2002.
Format/Description:
Book
1 online resource (ix, 270 pages) : digital, PDF file(s).
Series:
Cambridge tracts in mathematics ; 151.
Cambridge tracts in mathematics ; 151
Status/Location:
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Other Title:
Frobenius Manifolds & Moduli Spaces for Singularities
Subjects:
Singularities (Mathematics).
Frobenius algebras.
Moduli theory.
Language:
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:
Includes bibliographical references (p. 260-267) and index.
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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