A Geometric and Combinatorial Exploration of Hochschild Lattices

Hochschild lattices are specific intervals in the dexter meet-semilattices recently introduced by Chapoton. A natural geometric realization of these leads to some cell complexes Saneblidze, called polytopes. We obtain several geometrical properties lattices, namely we give cubic realizations, establish that EL-shellable, and show they constructible interval doubling. also prove combinatorial as enumeration their $k$-chains compute degree polynomials.