1206.1564 (Oliver Fabert)

Floer theory, Frobenius manifolds and integrable systems    [PDF]

Oliver Fabert

As shown by B. Dubrovin, the big quantum product, a generalization of the small quantum product involving the full rational Gromov-Witten potential, leads to infinite-dimensional integrable systems via the geometrical notion of Frobenius manifolds. In this paper we show how the big quantum product, Frobenius manifolds and the resulting integrable systems generalize from Gromov-Witten theory to the Floer theory of symplectomorphisms, extending the well-known relation between the small quantum product and the pair-of-pants product on Floer cohomology.

View original: http://arxiv.org/abs/1206.1564