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Combinatorics, Complexity, and ChanceA Tribute to Dominic Welsh$
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Geoffrey Grimmett and Colin McDiarmid

Print publication date: 2007

Print ISBN-13: 9780198571278

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198571278.001.0001

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ON THE UNKNOTTING PROBLEM

ON THE UNKNOTTING PROBLEM

Chapter:
(p.260) 16 ON THE UNKNOTTING PROBLEM
Source:
Combinatorics, Complexity, and Chance
Author(s):

Jorge Ramírez Alfonsín

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198571278.003.0016

This chapter discusses the methods, ideas, and viewpoints that have been used to investigate the unknotting problem. A knot is a closed simple (non-self-intersecting) curve embedded in the three-dimensional space. One of the most fundamental algorithmic questions about knots is the unknotting problem: the problem of how to decide whether a knot K is unknotted, that is, to decide whether K can be continuously deformed without self-intersection so that it lies in a plane. Despite a great deal of efforts, it is not known whether there exists an efficient algorithm for the unknotting problem.

Keywords:   unknotting problem, algorithm, braids, seifert circles, Reidemeister states, colour invariant

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