Turaev-Viro invariants and complexity of virtual 3-manifolds

Virtual 3-manifolds were introduced by S. Matveev in 2009 as a natural generalization of the classical 3-manifolds. In this talk we define the complexity of virtual 3-manifolds and calculate it for virtual 3-manifolds defined by special polyhedra with one, two and three 2-components. As a corollary, we establish the exact values of complexity for infinite families of hyperbolic 3-manifolds with geodesic boundary.
A part of the talk is based on a joint work with V. Turaev and A. Vesnin.