Dubrovin conjecture and the second structure connection

TL;DR

This paper reformulates the Dubrovin conjecture on quantum cohomology's semisimplicity using the second structure connection, introducing twisted reflection vectors to describe monodromy data elegantly.

Contribution

It provides a new reformulation of the Dubrovin conjecture and introduces twisted reflection vectors for analyzing monodromy data in quantum cohomology.

Findings

Reformulation of Dubrovin conjecture in terms of second structure connection

Introduction of twisted reflection vectors for monodromy analysis

Elegant description of monodromy data via Laplace transform

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.