ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 57M25 Hass, Joel, University of California, Davis USA and Lagarias, Jeff, AT&T Research, USA The number of Reidemeister Moves Needed for Unknotting There is a positive constant c_{1} such that for any diagram D representing the unknot, is a sequence of at most 2^{c_{1}n} Reidemeister moves that will convert it to a trivial knot diagram, where n is the number of crossings in D. A similar result holds for elementary moves on a polygonal knot K embedded in the 1-skeleton of the interior of a compact triangulated orientable P L 3-manifold M. There is a positive constant c_{2} such that for each t ≥ 1, if M consists of t tetrahedra, and K is unknotted, then there is a sequence of at most 2^{c_{2}t} elementary moves in M which transforms K to a triangle contained inside one tetrahedron of M. We obtain explicit values for c_{1} and c_{2}.