ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 17, 52, 57 Makarov, Vitalii S., Univ. Drujb. Narod., Russia Regular maps and hyperbolic 3-manifolds A hyperbolic 3-manifold M^{3} with symmetry group of order 28 800 is constructed. The map of this manifold is composed from 120 hyperbolic dodecahedra with dihedral angle 2π/5. It is shown that M^{3} is embedded (with self-intersections) into the hyperbolic four-dimensional manifold of regular 120-cells D^{4} (Davis manifold D^{4}). It is proved that the map of this 3manifold coincides with the map given by the incidence structure of 3-faces of four-dimensional regular star polytope {5, 3, 5/2}. Part of these results is joint work with F. Damian. Reference: F. L. Damian, and V. S. Makarov, Star polytopes and hyperbolic 3-manifolds Bul. Acad. de Ştiinţe a Rep. Moldova. Matematica (to appear).