Abstract
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.
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Fominykh, E.A. A Complete Description of Normal Surfaces for Infinite Series of 3-Manifolds. Siberian Mathematical Journal 43, 1112–1123 (2002). https://doi.org/10.1023/A:1021181720737
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DOI: https://doi.org/10.1023/A:1021181720737