Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

Volume 168 / 2001

Seiichi Kamada Fundamenta Mathematicae 168 (2001), 105-112 MSC: Primary 57Q45; Secondary 57M05, 57M25. DOI: 10.4064/fm168-2-1


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.


  • Seiichi KamadaDepartment 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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