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Geometry of Euclidean tetrahedra and knot invariants

Abstract

We construct knot invariants on the basis of ascribing Euclidean geometric values to a triangulation of the sphere S 3, where the knot lies. Edges of the triangulation along which the knot goes are distinguished by a nonzero deficit angle, in the terminology of the Regge calculus.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 4, pp. 105–117, 2005.

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Korepanov, I.G. Geometry of Euclidean tetrahedra and knot invariants. J Math Sci 144, 4437–4445 (2007). https://doi.org/10.1007/s10958-007-0282-3

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Keywords

  • Lens Space
  • Abelian Representation
  • CDAA
  • Acyclic Complex
  • Stellar Move