Real and integral structures in quantum cohomology I: toric orbifolds

Understand

We study real and integral structures in the space of solutions to the quantum differential equations.

• First we show that, under mild conditions, any real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry near the large radius limit.
• Secondly, we use mirror symmetry to calculate the "most natural" integral structure in quantum cohomology of toric orbifolds.
• We show that the integral structure pulled back from the singularity B-model is described only in terms of topological data in the A-model; K-group and a characteristic class.