Drinfeld-Manin Solutions Of The Yang-Baxter Equation Coming From Cube Complexes

The most common geometric interpretation of the Yang-Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are higher-dimensional cube complexes solving the D-state Yang-Baxter equation for arbitrarily large D. More precisely, we introduce explicit constructions of cube complexes covered by products of n trees and show that these cube complexes lead to new solutions of the Yang-Baxter equations.