DUKEIII

A program to handle edge-coloured graphs representing PL n-dimensional manifolds

One of the main features of crystallization theory relies on the purely combinatorial nature of the representing objects, which makes them particularly suitable for computer manipulation.

This fact allows a computational approach to the study of PL n-manifolds, which has been performed by means of several functions, collected in a unified program, called DUKE III.

DUKE III allows automatic manipulation of edge-coloured graphs representing PL n-manifolds (code computation, checking possible isomorphism between edge-coloured graphs, construction of boundary graph, checking bipartition, connectedness, rigidity and planarity conditions, combinatorial moves, invariants computation...).

Furthermore, DUKE III allows automatic recognition of orientable and non-orientable 3-manifolds triangulated by at most 30 coloured tetrahedra, making use of the existing electronic archives of all rigid bipartite and non-bipartite crystallizations up to 30 vertices (for details about generation and classification of crystallization catalogues, see:  CATALOGUES)

Download DUKE III (Windows .exe) program 

See also the SOFTWARE section.