Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 689-701 |
| Number of pages | 13 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 13 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Aug 1 2004 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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Blanlœil, V., Matsumoto, Y., & Saeki, O. (2004). Pull back relation for non-spherical knots. Journal of Knot Theory and its Ramifications, 13(5), 689-701. https://doi.org/10.1142/S0218216504003378