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Symplectic geometry of Frobenius structures

Alexander Givental
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Abstract

The purpose of the notes is to reiterate and expand the viewpoint, outlined in the paper math.AG/0110142 of T. Coates and the author, which recasts the concept of Frobenius manifold in terms of linear symplectic geometry and exposes the role of the twisted loop group L^{(2)}GL_N of hidden symmetries. New applications include a several line proof of the genus 0 Virasoro constraints and the quantum Hirzebruch-Riemann-Roch theorem in the theory of cobordism-valued Gromov-Witten invariants.

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BibTeXRIS

Alexander Givental. 2003-05-28. Symplectic geometry of Frobenius structures. https://arxiv.org/abs/math/0305409

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