Geodesic
Wirtinger presentations for higher dimensional manifold knots obtained from diagrams
Seiichi Kamada1
1 Department of Mathematics Osaka City University Sumiyoshi, Osaka 558-8585, Japan Current addres: Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688, U.S.A.
Fundamenta Mathematicae, Tome 168 (2001) no. 2, pp. 105-112.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

A Wirtinger presentation of a knot group is obtained from a diagram of the knot. T. Yajima showed that for a 2-knot or a closed oriented surface embedded in the Euclidean 4-space, a Wirtinger presentation of the knot group is obtained from a diagram in an analogous way. J. S. Carter and M. Saito generalized the method to non-orientable surfaces in 4-space by cutting non-orientable sheets of their diagrams by some arcs. We give a modification to their method so that one does not need to find and describe such arcs on the diagram. This method is easily generalized to higher dimensional manifold knots, which may not be locally flat.
DOI : 10.4064/fm168-2-1
Keywords: wirtinger presentation knot group obtained diagram knot yajima showed knot closed oriented surface embedded euclidean space wirtinger presentation knot group obtained diagram analogous carter saito generalized method non orientable surfaces space cutting non orientable sheets their diagrams arcs modification their method does describe arcs diagram method easily generalized higher dimensional manifold knots which may locally flat

Seiichi Kamada 1

1 Department of Mathematics Osaka City University Sumiyoshi, Osaka 558-8585, Japan Current addres: Department of Mathematics and Statistics University of South Alabama Mobile, AL 36688, U.S.A. 
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Seiichi Kamada. Wirtinger presentations for higher dimensional
manifold knots obtained from diagrams. Fundamenta Mathematicae, Tome 168 (2001) no. 2, pp. 105-112. doi : 10.4064/fm168-2-1. http://geodesic.mathdoc.fr/articles/10.4064/fm168-2-1/

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