ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57 Rasskazov, Alexey, Novosibirsk State University, Russia The structure of the canonical fundamental set for the 2-bridge link Let O(p/q, n) denote the orbifold with singular set the 2-bridge knot or link p/q and isotopy group cyclic of order n. The work is devoted to study of the fundamental set of the orbifold O(p/q, n) in the hyperbolic, Euclidean and spherical three-dimensional spaces. The main goal is to construct the simplest possible fundamental polyhedron for O(p/q, n) in the sense that it has just two pairs of mutually congruent curvelinear faces. The fundamental polyhedron is non-convex and consists of 2p tetrahedra whose vertices can be defined in a canonical way from the presentation of the orbifold fundamental group. It is joint work with A. Mednykh. Reference: A. Mednykh, A. Rasskazov, On the structure of the canonical fundamental set for the 2-bridge link orbifolds, Preprint 1997.