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Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

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Kamada S.

Fundamenta Mathematicae

2001

tom 168

nr 2

105-112

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.

Quandles and symmetric quandles for higher dimensional knots

100%

Kamada S.

Banach Center Publications

2014

tom 103

nr 1

145-158

A symmetric quandle is a quandle with a good involution. For a knot in ℝ³, a knotted surface in ℝ⁴ or an n-manifold knot in $ℝ^{n+2}$, the knot symmetric quandle is defined. We introduce the notion of a symmetric quandle presentation, and show how to get a presentation of a knot symmetric quandle from a diagram.

Ograniczanie wyników

1 Banach Center Publications

1 Fundamenta Mathematicae

2 Kamada S.

1 2014

1 2001

Wyniki wyszukiwania

Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

Quandles and symmetric quandles for higher dimensional knots