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Sibirskii Matematicheskii Zhurnal, 2002, Volume 43, Number 6, Pages 1372–1387
(Mi smj1377)
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A complete description of normal surfaces for infinite series of 3-manifolds
E. A. Fominykh Chelyabinsk State University
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.
Keywords:
normal surface, lens space, generalized quaternion space, Stallings manifold.
Received: 26.06.2002
Citation:
E. A. Fominykh, “A complete description of normal surfaces for infinite series of 3-manifolds”, Sibirsk. Mat. Zh., 43:6 (2002), 1372–1387; Siberian Math. J., 43:6 (2002), 1112–1123
Linking options:
https://www.mathnet.ru/eng/smj1377 https://www.mathnet.ru/eng/smj/v43/i6/p1372
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Abstract page: | 222 | Full-text PDF : | 80 |
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