Subject: Re: [TOP] Question about knot crossings Date: Mon, 19 Feb 2001 16:01:57 -0500 (EST) From: Joan Birman Responding to Sanderson's question: In "The number of Reidemeister moves needed for unknotting", Journal of the AMS, Jan 18, 2001, Hass and Legarias prove there is an algorithm which decides whether a knot is the unknot in $2^{cn}$ Reidemeister moves, where $c$ is bounded above by $10^{11}$. Their proof is based on the Haken machinery, improved by a key lemma of Jaco & Tollefson. Joan Birman