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＜電子ブック＞
Frobenius Manifolds : Quantum Cohomology and Singularities / edited by Claus Hertling, Matilde Marcolli
(Aspects of Mathematics ; 36)

版	1st ed. 2004.
出版者	(Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag)
出版年	2004
本文言語	英語
大きさ	XII, 378 p : online resource
著者標目	Hertling, Claus editor Marcolli, Matilde editor SpringerLink (Online service)
件　名	LCSH:Geometry, Differential LCSH:Geometry FREE:Differential Geometry FREE:Geometry
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-322-80236-1

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