01878510

j

01878510 Kovalevsky, Vladimir Multidimensional cell lists for investigating 3-manifolds. Discrete Appl. Math. 125, No.1, 25-43 (2003). 2003 Elsevier Science B.V. (North-Holland), Amsterdam EN I.4 topological properties of three-dimensional manifolds

doi:10.1016/S0166-218X(02)00222-6

Summary: 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.