Gamma-class is a program which implements the algorithm described in in [Casali M.R., Cristofori P., A catalogue of orientable 3-manifolds triangulated by 30 coloured tetrahedra, Journal of Knot Theory and its Ramifications 17 (2008), no.5, 579-599], with respect to a fixed (finite) set S of admissible sequences of elementary combinatorial moves: it yields, from any given list X of crystallizations, the automatic partition of the elements of X into equivalence classes, such that each class contains only crystallizations representing the same manifold. Moreover, the program tries the identification of the represented manifolds by means of comparison of the representatives of each class with known catalogues of crystallizations and/or splitting into connected sums.Program Gamma-class has already allowed the recognition and cataloguing of all manifolds represented by rigid bipartite and non bipartite crystallizations up to 30 vertices.
Gamma-class: A program to subdivide a set of rigid crystallizations of closed 3-manifolds into equivalence classes, whose elements represent homeomorphic manifolds / Casali, Maria Rita; Cristofori, Paola. - ELETTRONICO. - (2008).