Self-organized criticality and the lattice topology

We examine exhaustively the behavior of avalanches in critical height sandpile models based in two- and three-dimensional lattices of various topologies. We get that for two-dimensional lattices the spatial and temporal distributions characterizing bulk avalanches do not depend on the lattice topology. For the three-dimensional case, we detect a small dependence of the topology for the temporal distribution, while the spatial ones are independent. The two-dimensional lattices studied are: the plane (R2), the cylinder (S1 × R), and the Möbius-strip (M); and the three-dimensional are: R3, S1 × R2, S1 × S1 × R, M × R, S2 × R, K × R, and RP × R, where K and RP are, respectively, the Klein bottle and the real projective plane.