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© 2004

Frobenius Manifolds

Quantum Cohomology and Singularities

  • Klaus Hertling
  • Matilde Marcolli
Book

Part of the Aspects of Mathematics book series (ASMA, volume 36)

Table of contents

About this book

Introduction

Frobenius manifolds are complex manifolds with a multiplication and a metric on the holomorphic tangent bundle, which satisfy several natural conditions. This notion was defined in 1991 by Dubrovin, motivated by physics results. Another source of Frobenius manifolds is singularity theory. Duality between string theories lies behind the phenomenon of mirror symmetry. One mathematical formulation can be given in terms of the isomorphism of certain Frobenius manifolds. A third source of Frobenius manifolds is given by integrable systems, more precisely, bihamiltonian hierarchies of evolutionary PDE's. As in the case of quantum cohomology, here Frobenius manifolds are part of an a priori much richer structure, which, because of strong constraints, can be determined implicitly by the underlying Frobenius manifolds. Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems are flourishing areas since the early 90's. An activity was organized at the Max-Planck-Institute for Mathematics in 2002, with the purpose of bringing together the main experts in these areas. This volume originates from this activity and presents the state of the art in the subject.

Keywords

bihamiltonian hierarchies complex manifolds evolutionary PDE integrable systems isomorphism manifold metric multiplication singularity theory tangent bundle

Editors and affiliations

  • Klaus Hertling
    • 1
  • Matilde Marcolli
    • 2
  1. 1.Institut für Mathematik A 5, 6Universität MannheimMannheimGermany
  2. 2.Max-Planck-Institut für MathematikBonnGermany

About the editors

Prof. Dr. Claus Hertling, Institut für Mathematik, Universität Mannheim, Germany
Prof. Dr. Matilde Marcolli, Max-Planck-Institute for Mathematics, Bonn, Germany

Bibliographic information

  • Book Title Frobenius Manifolds
  • Book Subtitle Quantum Cohomology and Singularities
  • Editors Claus Hertling
    Matilde Marcolli
  • Series Title Aspects of Mathematics
  • DOI https://doi.org/10.1007/978-3-322-80236-1
  • Copyright Information Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden 2004
  • Publisher Name Vieweg+Teubner Verlag
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-528-03206-7
  • Softcover ISBN 978-3-322-80238-5
  • eBook ISBN 978-3-322-80236-1
  • Series ISSN 0179-2156
  • Edition Number 1
  • Number of Pages XII, 378
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Differential Geometry
    Geometry
  • Buy this book on publisher's site