2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/176117We construct an exactly solvable Hamiltonian acting on a 3-dimensional lattice of spin-$\frac 1 2$ systems that exhibits topological quantum order. The ground state is a string-net and a membrane-net condensate. Excitations appear in the form of quasiparticles and fluxes, as the boundaries of strings and membranes, respectively. The degeneracy of the ground state depends upon the homology of the 3-manifold. We generalize the system to $D\geq 4$, were different topological phases may occur. The whole construction is based on certain special complexes that we call colexes.Revtex4 file, color figures, minor correctionsStrongly Correlated ElectronsHigh Energy Physics - LatticeHigh Energy Physics - PhenomenologyHigh Energy Physics - TheoryQuantum Physicstext