Gromov - Witten invariants and quantization of quadratic hamiltonians

We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about Gromov-Witten invariants of compact symplectic manifolds and, more generally, Frobenius structures at...

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Bibliographic Details
Published in:arXiv.org 2001-10
Main Author: Givental, Alexander B
Format: Article
Language:English
Subjects:
Formalism
Invariants
Manifolds
Measurement
Online Access:Get full text
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Summary:We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about Gromov-Witten invariants of compact symplectic manifolds and, more generally, Frobenius structures at higher genus. We state several results illustrating the formalism and its use. In particular, we establish Virasoro constraints for semisimple Frobenius structures and outline a proof of the Virasoro conjecture for Gromov -- Witten invariants of complex projective spaces and other Fano toric manifolds. Details will be published elsewhere.
ISSN:2331-8422