ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57, 22 Vesnin, Andrei, Institute of Mathematics, Novosibisk, Russia On 3-manifolds with cyclic symmetry We discuss covering properties of manifolds uniformized by cyclically presented groups. Closed orientable three-dimensioanl manifolds M_{n}^{k/l} whose fundamental groups are Fractional Fibonacci groups

F^{k/l}(2, 2n) =< x_{1}, …, x_{2n}|x_{i}^{l}x_{i+1}^{k} = x_{i+2}^{l}, i = 1, …, 2n > are studied. Almost all of these manifolds are hyperbolic. Manifolds M_{n}^{1/l} are n-fold cyclic coverings of the sphere, branched over two-bridge knots K(2l + 1/2l). Part of these results is joint work with A. Kim. Reference: A. Vesnin, and A. Kim, Fractional Fibonacci groups and manifolds, Siberian Math. J. 39(4) (1998).