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Self-linking of spatial curves without inflections and its applications

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Functional Analysis and Its Applications Aims and scope

Abstract

The self-linking number of generic smooth closed curves in Euclidean 3-space is studied. A formula expressing the self-linking number via the signs of the double points of a generic projection of the curve on a plane and the signs of the torsion at the points that are projected into inflection points is obtained. Every local invariant of generic curves is proved to be equal, up to an additive constant, to a linear combination of two basic local invariants: the number of flattening points and the self-linking number.

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Authors
  1. F. Aicardi
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Additional information

Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 34, No. 2, pp. 1–8, April–June, 2000.

Translated by F. Aicardi

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Aicardi, F. Self-linking of spatial curves without inflections and its applications. Funct Anal Its Appl 34, 79–85 (2000). https://doi.org/10.1007/BF02482420

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  • DOI: https://doi.org/10.1007/BF02482420

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