Different moment-angle manifolds arising from two polytopes having the same bigraded Betti numbers

Abstract

Two simple polytopes of dimension $3$ having identical bigraded Betti numbers but nonisomorphic Tor–algebras are presented. These polytopes provide two homotopically different moment-angle manifolds having the same bigraded Betti numbers. These two simple polytopes are the first examples of polytopes that are (toric) cohomologically rigid but not combinatorially rigid.