Flat 3-webs via semi-simple Frobenius 3-folds

TL;DR

This paper constructs flat 3-webs from semi-simple Frobenius 3-folds, interprets their Chern connection geometrically, and shows they are hexagonal webs with symmetries, linking them to solutions of associativity equations.

Contribution

It introduces a geometric construction of flat 3-webs from semi-simple Frobenius manifolds and analyzes their properties and singularities.

Findings

Webs are biholomorphic to characteristic webs of associativity equations

Webs are hexagonal and have at least one infinitesimal symmetry at each singularity

Singularities of the webs are characterized and discussed

Abstract

We construct flat 3-webs via semi-simple geometric Frobenius manifolds of dimension three and give geometric interpretation of the Chern connection of the web. These webs turned out to be biholomorphic to the characteristic webs on the solutions of the corresponding associativity equation. We show that such webs are hexagonal and admit at least one infinitesimal symmetry at each singular point. Singularities of the web are also discussed.