Abstract: This paper presents a general lossless connectivity compression scheme for manifolds in any dimension with arbitrary cells, orientable or not, with or without borders. Relying on a generic topological model called generalized maps, our method performs a region-growing traversal of its primitive elements while describing connectivity relations with symbols. The set of produced symbols is compressed using standard data compression techniques. These algorithms have been successfully applied to various models (surface, tetrahedral and hexahedral meshes), showing the efficiency and genericity of the proposed scheme.