Siberian Mathematical Journal

, Volume 43, Issue 6, pp 1112–1123 | Cite as

A Complete Description of Normal Surfaces for Infinite Series of 3-Manifolds

  • E. A. Fominykh


The set of all normal surfaces in a 3-manifold is a partial monoid under addition with a minimal generating set of fundamental surfaces. The available algorithm for finding the system of fundamental surfaces is of a theoretical nature and admits no implementation in practice. In this article, we give a complete and geometrically simple description for the structure of partial monoids for normal surfaces in lens spaces, generalized quaternion spaces, and Stallings manifolds with fiber a punctured torus and a hyperbolic monodromy map.

normal surface lens space generalized quaternion space Stallings manifold 


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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • E. A. Fominykh
    • 1
  1. 1.Chelyabinsk State UniversityRussia

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