Geodesic
Complexity of virtual 3-manifolds
Sbornik. Mathematics, Tome 207 (2016) no. 11, pp. 1493-1511

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Virtual $3$-manifolds were introduced by Matveev in 2009 as natural generalizations of classical $3$-manifolds. In this paper, we introduce a notion of complexity for a virtual $3$-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two $2$-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic $3$-manifolds with totally geodesic boundary. Bibliography: 24 titles.
Keywords: virtual manifolds, $3$-manifolds, hyperbolic manifolds, complexity. 
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     author = {A. Yu. Vesnin and V. G. Turaev and E. A. Fominykh},
     title = {Complexity of virtual 3-manifolds},
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     url = {http://geodesic.mathdoc.fr/item/SM_2016_207_11_a1/}
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A. Yu. Vesnin; V. G. Turaev; E. A. Fominykh. Complexity of virtual 3-manifolds. Sbornik. Mathematics, Tome 207 (2016) no. 11, pp. 1493-1511. http://geodesic.mathdoc.fr/item/SM_2016_207_11_a1/