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Frobenius Manifolds: Quantum Cohomology and Singularities

Frobenius Manifolds: Quantum Cohomology and Singularities
Catalogue Information
Field name Details
Dewey Class 516.36
Title Frobenius Manifolds ([EBook] :) : Quantum Cohomology and Singularities / / edited by Klaus Hertling, Matilde Marcolli.
Added Personal Name Hertling, Klaus editor.
Marcolli, Matilde editor.
Other name(s) SpringerLink (Online service)
Publication Wiesbaden : : Vieweg+Teubner Verlag, , 2004.
Physical Details XII, 378 p. : online resource.
Series Aspects of mathematics 0179-2156 ; ; 36
ISBN 9783322802361
Summary Note 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.:
Contents note Gauss-Manin systems, Brieskorn lattices and Frobenius structures (II) -- Opposite filtrations, variations of Hodge structure, and Frobenius modules -- The jet-space of a Frobenius manifold and higher-genus Gromov-Witten invariants -- Symplectic geometry of Frobenius structures -- Unfoldings of meromorphic connections and a construction of Probenius manifolds -- Discrete torsion, symmetric products and the Hubert scheme -- Relations among universal equations for Gromov-Witten invariants -- Extended modular operad -- Operads, deformation theory and F-manifolds -- Witten’s top Chern class on the moduli space of higher spin curves -- Uniformization of the orbifold of a finite reflection group -- The Laplacian for a Frobenius manifold -- Virtual fundamental classes, global normal cones and Fulton’s canonical classes -- A note on BPS invariants on Calabi-Yau 3-folds -- List of Participants.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-3-322-80236-1
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