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A New Means for Investigating 3-Manifolds

  • Vladimir Kovalevsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

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 three-dimensional case. Some experimental results are presented.

Keywords

Fundamental Group Hausdorff Space Dimensional Sphere Incidence Structure Classical Topology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Vladimir Kovalevsky
    • 1
  1. 1.Institute of Computer GraphicsUniversity of RostockRostockGermany

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