Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

• Autorzy: Seiichi Kamada
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57Q45: Knots and links (in high dimensions)
• 57M25: Knots and links in S 3
• 57M05: Fundamental group, presentations, free differential calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 168
• Numer: 2
• Strony: 105-112

Daty

wydano

2001

Twórcy

autor

Seiichi Kamada

• Department of Mathematics, Osaka City University, Sumiyoshi, Osaka 558-8585, Japan
• Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, U.S.A.

Identyfikatory

DOI

10.4064/fm168-2-1