Geometric presentations of classical knot groups

John Erbland and Mauricio Guterriez

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-4

Abstract:

The question addressed by thls paper is, how close is the tunnel number of a knot to the minimum number of relators in a presentation of the knot group? A dubious, but useful conjecture, is that these two invariants are equal. (The analogous assertion applied to 3-manifolds is known to be false. [1]). It has been shown recently [2] that not all presentations of a knot group are geometric. The main result in this paper asserts that the tunnel number is equal to the minimum number of relators among presentations satisfying a somewhat restrictive condition, that is, that such presentations are always geometric.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:547297

DOI: 10.1155/S0161171291000339

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