Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The number of Reidemeister moves needed for unknotting
HTML articles powered by AMS MathViewer

by Joel Hass and Jeffrey C. Lagarias
J. Amer. Math. Soc. 14 (2001), 399-428
DOI: https://doi.org/10.1090/S0894-0347-01-00358-7
Published electronically: January 18, 2001

Abstract:

There is a positive constant $c_1$ such that for any diagram $\mathcal {D}$ representing the unknot, there 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 $\mathcal {D}$. 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 $c_2$ such that for each $t \geq 1$, 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 $c_2$.
References
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (1991): 57M25, 11Y16, 68W40
  • Retrieve articles in all journals with MSC (1991): 57M25, 11Y16, 68W40
Bibliographic Information
  • Joel Hass
  • Affiliation: Department of Mathematics, University of California, Davis, California 95616
  • Address at time of publication: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
  • Email: hass@math.ucdavis.edu
  • Jeffrey C. Lagarias
  • Affiliation: AT&T Labs – Research, Florham Park, New Jersey 07932
  • MR Author ID: 109250
  • Email: jcl@research.att.com
  • Received by editor(s): May 8, 1998
  • Received by editor(s) in revised form: October 10, 2000
  • Published electronically: January 18, 2001
  • Additional Notes: The first author was partially supported by NSF grant DMS-9704286.
    This paper grew out of work begun while the authors were visiting the Mathematical Sciences Research Institute in Berkeley in 1996/97. Research at MSRI was supported in part by NSF grant DMS-9022140.
  • © Copyright 2001 AT&T Corp.
  • Journal: J. Amer. Math. Soc. 14 (2001), 399-428
  • MSC (1991): Primary 57M25; Secondary 11Y16, 68W40
  • DOI: https://doi.org/10.1090/S0894-0347-01-00358-7
  • MathSciNet review: 1815217