CRYSTALLIZATION CATALOGUES AND ARCHIVES OF CLOSED 3-MANIFOLDS WITH LOW GEM-COMPLEXITY

CRYSTALLIZATION CATALOGUES is a collection of algorithmic procedures, which can be used to construct essential catalogues of bipartite and/or non bipartite edge-coloured graphs representing all orientable and/or non orientable 3-manifolds triangulated by a given number of coloured tetrahedra; the elements of the obtained catalogues may further be classified (i.e. subdivided into homeomorphism classes), as a first step toward the topological recognition of the involved manifolds. The output data of the C++ program (originally described in [M.R.Casali, Classification of non-orientable 3-manifolds admitting decompositions into 26 coloured tetrahedra, Acta Appl. Math. 54 (1999), 75-97]) generating catalogue C^2p of rigid bipartite crystallizations up to 2p vertices and/or catalogue ~C^2p of rigid non bipartite crystallizations up to 2p vertices are available, according to the number of vertices, at the Web page: http://cdm.unimo.it/home/matematica/casali.mariarita/CATALOGUES.htmThe Web page contains detailed results about existing catalogues ~C^26, C^28 and C^30 which are not included in the associated papers (for example: complete description of the involved manifolds, survey tables with related topological invariants, data about the reduced catalogues of cluster-less crystallizations…). Further, a comparative analysis of both complexity and geometric properties of manifolds represented by the subsequent subsets C^2p, p compreso tra 1 e 15, of all crystallizations in C^30 with exactly 2p vertices is also presented.