Self-organized criticality and the lattice topology

We examine exhaustively the behavior of avalanches in critical height sandpile models based in twoand 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 twodimensional 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. PACS: 05.40.+j, 64.60.Ht, 05.60.+w