J Austral Math Soc Ser A 56 pp1--16, 1994.

Knot Projections and Coexter Groups

A. M. Brunner and Y. W. Lee

Abstract

Every knot admits a special projection with the property that under the projection discs in the cacnonical 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 Coexeter 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 criterion to decide when an inseparable projection with 3 discs comes from the trivial knot.

1991 AMS Subject Classification: primary 57M25; secondary 20F35

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Authors

A. M. Brunner

Department of Mathematics, University of Wisconsin-Parkside, Kenosha, Wisconsin 53141, U.S.A.

Y. W. Lee

Department of Mathematics, University of Wisconsin-Parkside, Kenosha, Wisconsin 53141, U.S.A.