Dubrovin conjecture and the second structure connection

Abstract

We give a reformulation of the Dubrovin conjecture about the semisimplicity of quantum cohomology in terms of the so-called second structure connection of quantum cohomology. The key ingredient in our work is the notion of a twisted reflection vector which allows us to give an elegant description of the monodromy data of the quantum connection in terms of the monodromy data of its Laplace transform.

45 pages, various typos were fixed, more details were given in some of the proofs, this version is accepted in Journal of Geometry and Physics