Knots, i.e. embeddings of spheres
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For notation and conventions throughout this page see [[High_codimension_embeddings|high codimension embeddings]]. | For notation and conventions throughout this page see [[High_codimension_embeddings|high codimension embeddings]]. | ||
== Examples == | == Examples == | ||
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Revision as of 12:39, 26 October 2016
This page has not been refereed. The information given here might be incomplete or provisional. |
For notation and conventions throughout this page see high codimension embeddings.
1 Examples
Analogously to the Haefliger trefoil knot for one constructs a smooth embedding . For even this embedding is a generator of ; it is not smoothly isotopic to the standard embedding, but is piecewise smoothly isotopic to it [Haefliger1962]. It would be interesting to know if for odd this embedding is a generator of . The last phrase of [Haefliger1962t] suggests that this is true for .
2 Classification
(I would suggest including the classification of simple knots a la Kearton et. al. in this section.---John Klein)
3 References
- [Haefliger1962] A. Haefliger, Knotted -spheres in -space, Ann. of Math. (2) 75 (1962), 452–466. MR0145539 (26 #3070) Zbl 0105.17407
- [Haefliger1962t] A. Haefliger, Differentiable links, Topology, 1 (1962) 241--244