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Finite-order invariants of ornaments

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Abstract

Anornament is a collection of oriented closed curves in a plane, no three of which intersect at the same point. We consider homotopy invariants of ornaments. Thefinite-order invariants of ornaments are a natural analog of the Vassiliev invariants of links. The calculation of them is based on the homological study of the corresponding space of singular objects. We perform the “local” part of these calculations and a part of the “global” one, which allows us to estimate the dimensions of the spaces of invariants of any order. We also construct explicity two large series of such invariants and establish some new algebraic structures in the space of invariants.

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Authors
  1. A. B. Merkov
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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 35, Algebraicheskaya Geometriya-6, 1996.

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Merkov, A.B. Finite-order invariants of ornaments. J Math Sci 90, 2215–2273 (1998). https://doi.org/10.1007/BF02433952

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