New aspects of complexity theory for 3-manifolds

A. Yu. Vesnin; S. V. Matveev; E. A. Fominykh

A. Yu. Vesnin ; S. V. Matveev ; E. A. Fominykh

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 4, pp. 615-660 Cet article a éte moissonné depuis la source Math-Net.Ru

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Résumé

Recent developments in the theory of complexity for three-dimensional manifolds are reviewed, including results and methods that emerged over the last decade. Infinite families of closed orientable manifolds and hyperbolic manifolds with totally geodesic boundary are presented, and the exact values of the Matveev complexity are given for them. New methods for computing complexity are described, based on calculation of the Turaev–Viro invariants and hyperbolic volumes of 3-manifolds. Bibliography: 89 titles.

Keywords: 3-manifolds, Matveev complexity, tetrahedral complexity, spines.
Mots-clés : triangulations

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A. Yu. Vesnin; S. V. Matveev; E. A. Fominykh. New aspects of complexity theory for 3-manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 73 (2018) no. 4, pp. 615-660. http://geodesic.mathdoc.fr/item/RM_2018_73_4_a1/

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