TY - JOUR
T1 - Pull back relation for non-spherical knots
AU - Blanlœil, Vincent
AU - Matsumoto, Yukio
AU - Saeki, Osamu
N1 - Funding Information:
The third author has been partially supported by the Louis Pasteur University of Strasbourg. He would like to express his thanks to the people at the Louis Pasteur University of Strasbourg, France, for their hospitality during the preparation of the manuscript.
PY - 2004/8
Y1 - 2004/8
N2 - We introduce a new relation for high dimensional non-spherical knots, which is motivated by the codimension two surgery theory: a knot is a pull back of another knot if the former is obtained as the inverse image of the latter by a certain degree one map between the ambient spheres. We show that this relation defines a partial order for (2n - 1)-dimensional simple fibered knots for n ≥ 3. We also give some related results concerning cobordisms and isotopies of knots together with several important explicit examples.
AB - We introduce a new relation for high dimensional non-spherical knots, which is motivated by the codimension two surgery theory: a knot is a pull back of another knot if the former is obtained as the inverse image of the latter by a certain degree one map between the ambient spheres. We show that this relation defines a partial order for (2n - 1)-dimensional simple fibered knots for n ≥ 3. We also give some related results concerning cobordisms and isotopies of knots together with several important explicit examples.
UR - http://www.scopus.com/inward/record.url?scp=7444240277&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=7444240277&partnerID=8YFLogxK
U2 - 10.1142/S0218216504003378
DO - 10.1142/S0218216504003378
M3 - Article
AN - SCOPUS:7444240277
VL - 13
SP - 689
EP - 701
JO - Journal of Knot Theory and its Ramifications
JF - Journal of Knot Theory and its Ramifications
SN - 0218-2165
IS - 5
ER -