1998/07/02 by Joel Hass, Jeffrey C. Lagarias
Mathematics · #math.GT #msc:57M25 #msc:68Q25
published as J. Amer. Math. Soc. 14 (2001), 399--428. · 48 pages, 14 figures
arxiv created 1998/07/02 · arxiv updated 2009/11/30
There is a positive constant c1 such that for any diagram D representing the unknot, there is a sequence of at most 2c1 n Reidemeister moves that will convert it to a trivial knot diagram, 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, orientable, triangulated PL 3-manifold M. There is a positive constant c2 such that for each t ≥ 1, if M consists of t tetrahedra, and K is unknotted, then there is a sequence of at most 2c2 t elementary moves in M which transforms K to a triangle contained inside one tetrahedron of M. We obtain explicit values for c1 and c2.