Complexity of virtual 3-manifolds

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.