An algorithm for checking property P for knots with complements of Heegaard genus 2

Osborne, R. P.

doi:10.1090/S0002-9939-1983-0695275-8

An algorithm for checking property P for knots with complements of Heegaard genus $2$
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Proc. Amer. Math. Soc. 88 (1983), 357-362 Request permission

Abstract:

One of the most fundamental questions about knots is: If we know the topological type of the complement of a knot, is the knot determined? In this paper we give an algorithm for deciding if certain knots called tunnel number one knots are determined by their complements. This algorithm turns out to be practical and efficient in that it can be used on knots with ten crossings without the aid of a computer and one can expect to be able to handle knots with, say, twenty crossings with the aid of a desk-top computer.

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