Wirtinger presentations for higher dimensional manifold knots obtained from diagrams

@article{SeiichiKamada2001,
abstract = {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.},
author = {Seiichi Kamada},
journal = {Fundamenta Mathematicae},
keywords = {Wirtinger presentation; knot group; higher dimensional knot; knot diagram; broken surface diagram},
language = {eng},
number = {2},
pages = {105-112},
title = {Wirtinger presentations for higher dimensional manifold knots obtained from diagrams},
url = {http://eudml.org/doc/282505},
volume = {168},
year = {2001},
}

TY - JOUR
AU - Seiichi Kamada
TI - Wirtinger presentations for higher dimensional manifold knots obtained from diagrams
JO - Fundamenta Mathematicae
PY - 2001
VL - 168
IS - 2
SP - 105
EP - 112
AB - 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.
LA - eng
KW - Wirtinger presentation; knot group; higher dimensional knot; knot diagram; broken surface diagram
UR - http://eudml.org/doc/282505
ER -