# Frobenius Manifolds: Quantum Cohomology and Singularities

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*Claus Hertling; Matilde Marcolli*

A publication of Vieweg+Teubner

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.

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.