ON THE UNKNOTTING PROBLEM
ON THE UNKNOTTING PROBLEM
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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