• Corpus ID: 17026531

Spaces of Knots

@article{Hatcher1999SpacesOK,
  title={Spaces of Knots},
  author={Allen Hatcher},
  journal={arXiv: Geometric Topology},
  year={1999}
}
  • A. Hatcher
  • Published 16 September 1999
  • Mathematics
  • arXiv: Geometric Topology
We consider the space of all smooth knots in the 3-sphere isotopic to a given knot, with the aim of finding a small subspace onto which this large space deformation retracts. For torus knots and many hyperbolic knots we show the subspace can be taken to be the orbit of a single maximally symmetric placement of the knot under the action of SO(4) by rotations of the ambient 3-sphere. This would hold for all hyperbolic knots if it were known that there are no exotic free actions of a finite cyclic… 

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Sur le groupe fondamental de l'espace des noeuds

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Eine Kennzeichnung der Torusknoten