Classification of Nonorientable 3-Manifolds Admitting Decompositions into ≤ 26 Coloured Tetrahedra |
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Authors: | Maria Rita Casali |
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Affiliation: | (1) Dipartimento di Matematica Pura ed Applicata, Università di Modena, Via Campi 213 B, I-41100 Modena, Italy |
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Abstract: | The present paper adopts a computational approach to the study of nonorientable 3-manifolds: in fact, we describe how to create an automaticcatalogue of all nonorientable 3-manifolds admitting coloured triangulationswith a fixed number of tetrahedra. In particular, the catalogue has been effectively produced and analysed for up to 26 tetrahedra, to reach the complete classification of all involved 3-manifolds. As a consequence, the following summarising result can be stated:THEOREM I. Exactly seven closed connected prime nonorientable3-manifolds exist, which admit a coloured triangulation consisting of atmost 26 tetrahedra.More precisely, they are the four Euclidean nonorientable 3-manifolds, the nontrivial S2 bundle overS1, the topological product between thereal projective plane RP2 andS1, and the torus bundle overS1, with monodromy induced by matrix(10 -11). |
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Keywords: | nonorientable 3-manifold crystallization coloured triangulation gem-complexity |
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