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Frobenius Manifolds: Quantum Cohomology and Singularities

Edited by: Claus Hertling Universität Mannheim, Mannheim, Germany
Matilde Marcolli Max Planck Institute forMathematics, Bonn, Germany
A publication of Vieweg+Teubner
Available Formats:
Hardcover ISBN: 978-3-528-03206-7
Product Code: VWAM/36
378 pp
List Price: $121.00 AMS Member Price:$108.90
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Frobenius Manifolds: Quantum Cohomology and Singularities
Edited by: Claus Hertling Universität Mannheim, Mannheim, Germany
Matilde Marcolli Max Planck Institute forMathematics, Bonn, Germany
A publication of Vieweg+Teubner
Available Formats:
 Hardcover ISBN: 978-3-528-03206-7 Product Code: VWAM/36 378 pp
 List Price: $121.00 AMS Member Price:$108.90
• Book Details

Vieweg Aspects of Mathematics
Volume: 362004
MSC: Primary 53; 14; Secondary 37; 34; 32;

Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems have been flourishing areas since the early 1990s. A conference was organized at the Max-Planck-Institute for Mathematics to bring together leading experts in these areas. This volume originated from that meeting and presents the state of the art in the subject.

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.

This volume is suitable for graduate students and research mathematicians interested in geometry and topology.

Graduate students and research mathematicians interested in geometry and topology.

• Request Review Copy
Volume: 362004
MSC: Primary 53; 14; Secondary 37; 34; 32;

Quantum cohomology, the theory of Frobenius manifolds and the relations to integrable systems have been flourishing areas since the early 1990s. A conference was organized at the Max-Planck-Institute for Mathematics to bring together leading experts in these areas. This volume originated from that meeting and presents the state of the art in the subject.

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.

This volume is suitable for graduate students and research mathematicians interested in geometry and topology.