Frobenius manifolds and moduli spaces for singularities / Claus Hertling. [electronic resource]
 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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Details
 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 Fmanifolds
Finitedimensional algebras
Vector bundles with multiplication
Definition of Fmanifolds
Decomposition of Fmanifolds and examples
Fmanifolds and potentiality
Massive Fmanifolds and Lagrange maps
Lagrange property of massive Fmanifolds
Existence of Euler fields
LyashkoLooijenga maps and graphs of Lagrange maps
Miniversal Lagrange maps and Fmanifolds
LyashkoLooijenga map of an Fmanifold
Discriminants and modality of Fmanifolds
Discriminant of an Fmanifold
2dimensional Fmanifolds
Logarithmic vector fields
Isomorphisms and modality of germs of Fmanifolds
Analytic spectrum embedded differently
Singularities and Coxeter groups
Hypersurface singularities
Boundary singularities
Coxeter groups and Fmanifolds
Coxeter groups and Frobenius manifolds
3dimensional and other Fmanifolds
Frobenius manifolds, GaussManin 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
RiemannHilbertBirkhoff 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. 260267) and index.
Title from publisher's bibliographic system (viewed on 05 Oct 2015).  ISBN:
 1107125642
1280434015
0511045417
9786610434015
0511147740
0511177410
0511305001
0511543107  OCLC:
 559254871