Vieweg Aspects of Mathematics 2004; 378 pp; hardcover Volume: 36 ISBN10: 3528032065 ISBN13: 9783528032067 List Price: US$121 Member Price: US$108.90 Order Code: VWAM/36
 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 MaxPlanckInstitute 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. A publication of Vieweg+Teubner. The AMS is exclusive distributor in North America. Vieweg+Teubner Publications are available worldwide from the AMS outside of Germany, Switzerland, Austria, and Japan. Readership Graduate students and research mathematicians interested in geometry and topology. Table of Contents  A. Douai and C. Sabbah  GaussManin systems, Brieskorn lattices and Frobenius structures (II)
 J. Fernandez and G. Pearlstein  Opposite filtrations, variations of Hodge structure, and Frobenius modules
 E. Getzler  The jetspace of a Frobenius manifold and highergenus GromovWitten invariants
 A. B. Givental  Symplectic geometry of Frobenius structures
 C. Hertling and Yu. I. Manin  Unfoldings of meromorphic connections and a construction of Frobenius manifolds
 R. Kaufmann  Discrete torsion, symmetric products and the Hilbert scheme
 X. Liu  Relations among universal equations for GromovWitten invariants
 A. Losev and Yu. I. Manin  Extended modular operad
 S. Merkulov  Operads, deformation theory and Fmanifolds
 A. Polishchuk  Witten's top Chern class on the moduli space of higher spin curves
 K. Saito  Uniformization of the orbifold of a finite reflection group
 I. Satake  The Laplacian for a Frobenius manifold
 B. Siebert  Virtual fundamental classes, global normal cones and Fulton's canonical classes
 A. Takahashi  A note on BPS invariants on CalabiYau 3folds
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