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Complexity Theory of 3-Manifolds

  • Sergei Matveev
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 9)

Abstract

Denote by M the set of all compact 3-manifolds. We wish to study it systematically and comprehensively. The crucial question is the choice of filtration in M. It would be desirable to have a finite number of 3-manifolds in each term of the filtration, all of them being in some sense simpler than those in the subsequent terms. A useful tool here would be a measure of “complexity” of a 3-manifold. Given such a measure, we might hope to enumerate all ‘simple’ manifolds before moving on to more complicated ones. There are several well-known candidates for such a complexity function. For example, take the Heegaard genus g(M), defined to be the minimal genus over all Heegaard decompositions of M. Other examples include the minimal number of sim-plices in a triangulation of M and the minimal crossing number in a surgery presentation for M.

Keywords

Boundary Curve Lens Space Solid Torus Regular Neighborhood Special Spine 
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 2003

Authors and Affiliations

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

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