Multidimensional cell lists for investigating 3-manifolds Original Research Article

The paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as block complexes. The paper contains definitions and a theorem necessary to transfer some basic knowledge of the classical topology to finite topological spaces. The method is based on subdividing the given set into blocks of cells in such a way that a k-dimensional block be homeomorphic to a k-dimensional ball. The block structure is described by the data structure known as “cell list” which is generalized here for the multidimensional case. Results of computer experiments are presented.