Frobenius manifolds and moduli spaces for singularities [E-Book] / Claus Hertling.
Hertling, Claus, (author)
Cambridge : Cambridge University Press, 2002
1 online resource (ix, 270 pages)
Cambridge tracts in mathematics ; 151
Full Text
Table of 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.