 

ChanHo Suh
Boundarytwisted normal form and the number of elementary moves to unknot view print


Published: 
June 4, 2012 
Keywords: 
Reidemeister move, unknotting, normal surface 
Subject: 
Primary 57M, 57N10; Secondary 68Q25 


Abstract
Suppose K is an unknot lying in the 1skeleton of a triangulated 3manifold with t tetrahedra. Hass and Lagarias showed there is an upper bound, depending only on t, for the minimal number of elementary moves to untangle K. We give a simpler proof, utilizing a normal form for surfaces whose boundary is contained in the 1skeleton of a triangulated 3manifold. We also obtain a significantly better upper bound of 2^{120t+14} and improve the HassLagarias upper bound on the number of Reidemeister moves needed to unknot to 2^{105 n}, where n is the crossing number.


Acknowledgements
Research was partially funded by the National Science Foundation (VIGRE DMS0135345 and DMS0636297).


Author information
University of California, One Shields Avenue, Davis, CA 95616
suh@math.ucdavis.edu

