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.
Publié le : 2004-07-05
Classification:
Pull back,
codimension two surgery,
high dimensional knot,
cobordism,
fibered knot,
57Q45, 57R40, 57R65,
[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]
@article{hal-00084338,
author = {Blanloeil, Vincent and Matsumoto, Yukio and Saeki, Osamu},
title = {Pull back relation for non-spherical knots},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00084338}
}
Blanloeil, Vincent; Matsumoto, Yukio; Saeki, Osamu. Pull back relation for non-spherical knots. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00084338/