Knot projections and Coxeter groups
1994 ◽
Vol 56
(1)
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pp. 1-16
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AbstractEvery knot admits a special projection with the property that under the projection discs in the canonical Seifert surface project disjointly. Under an isotopy, such a projection can be turned into a connected sum of what we call inseparable projections. The main result is that if there is no band in an inseparable projection with half-twisting number +1 or −1, then the projection is not a projection of the trivial knot. To prove this a non-cyclic Coxeter group is constructed as a quotient of the knot group. The construction is possibly of interest in itself. The techniques developed are applied to give a criterion to decide when an inseparable projection with 3 discs comes from the trivial knot.
2014 ◽
Vol 66
(2)
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pp. 354-372
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2011 ◽
Vol 16
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pp. 82
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2019 ◽
Vol 75
(3)
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pp. 584-592
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1982 ◽
Vol 26
(1)
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pp. 1-15
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Keyword(s):
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2005 ◽
Vol 79
(1)
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pp. 141-147
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2000 ◽
Vol 24
(12)
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pp. 821-823
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