Geometric presentations of classical knot groups
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]...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000339 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |