A New Means for Investigating 3-Manifolds

The paper presents a new method of investigating topological properties of three-dimensional manifolds by means of computers. Manifolds are represented as finite cell 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 simple 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 threedimensional case. Some experimental results are presented.

• Type: Conference
• Year: 2000
• Where: DGCI
• Authors: Vladimir Kovalevsky
• Keywords: DGCI 2000, Discrete Geometry, Finite Cell Complexes, Paper Contains Definitions, Topological Properties