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Translator’s Introduction 6

In: Papers on Group Theory and Topology

Author

Listed:
  • Max Dehn

Abstract

Of all Dehn’s results, perhaps the one most understandable to a non-mathematician is the following: a left-hand trefoil knot cannot be deformed into a right-hand trefoil knot. The statement concerns everyday objects, and only the proof is difficult. Dehn’s proof is based on the observation that a deformation of one trefoil knot to the other would induce an automorphism of the knot group which associates certain geometrically significant elements, namely “latitude” and “longitude” curves on the neighbourhood torus of the knot, which determine an orientation of the ambient space.

Suggested Citation

  • Max Dehn, 1987. "Translator’s Introduction 6," Springer Books, in: Papers on Group Theory and Topology, pages 200-202, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4668-8_11
    DOI: 10.1007/978-1-4612-4668-8_11
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