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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory