Computer Presentation of 3-Manifolds

  • Sergei Matveev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2243)


Our goal is to describe an economic way of presenting 3-manifolds numerically. The idea consists in replacing 3-manifolds by cell complexes (their special spines) and encoding the spines by strings of integers. The encoding is natural, i.e., it allows one to operate with manifolds without decoding. We describe an application of the encoding to computer enumeration of 3-manifolds and give the resulting table. A brief introduction into the theory of quantum invariants of 3-manifolds is also given. The invariants were used by the enumeration for auto-matic casting out of duplicates. Separately, we investigate 3-dimensional submanifolds of R 3. Any such submanifold can be presented by a 3-di-mensional binary picture. We give a criterion for a 3-dimensional binary picture to determine a 3-manifold.


Regular Graph Cell Complex Homology Sphere Special Spine Lattice Cube 
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© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Sergei Matveev
    • 1
  1. 1.Chelyabinsk State UniversityChelyabinskRussia

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