Complexity of virtual 3-manifolds
Abstract
Virtual $3$-manifolds were introduced by S.V. Matveev in 2009 as natural generalizations of the classical $3$-manifolds. In this paper, we introduce a notion of complexity of 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2016
- DOI:
- 10.48550/arXiv.1609.06813
- arXiv:
- arXiv:1609.06813
- Bibcode:
- 2016arXiv160906813F
- Keywords:
-
- Mathematics - Geometric Topology;
- 57M27;
- 57M50;
- 57M20
- E-Print:
- 19 pages