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This article is cited in 6 scientific papers (total in 6 papers)
Segment-arrow diagrams and invariants of ornaments
A. B. Merkov Institute of Systems Analysis, Russian Academy of Sciences
Abstract:
An ornament is a finite collection of closed oriented curves in the plane no three of which have common points. Homotopy invariants of ornaments are considered. Similarly to the case of knot classification, all invariants of ornaments are equal to the linking numbers with appropriate cycles in the discriminant, that is, in the set of collections of curves with forbidden intersections. Finite-order (or Vassiliev) invariants are those for which the corresponding cycle can be described in terms of finitely many strata in the natural stratification of the discriminant by the types of forbidden points. The calculation of these invariants is reduced to the calculation of certain cohomological spectral sequences.
A new explicit combinatorial construction of a series of finite order invariants of ornaments is presented. It is shown that some previously known series of finite order invariants are contained in this series, which can also be expressed in terms of cohomology classes of natural finite-dimensional topological spaces.
Received: 24.01.2000
Citation:
A. B. Merkov, “Segment-arrow diagrams and invariants of ornaments”, Mat. Sb., 191:11 (2000), 47–78; Sb. Math., 191:11 (2000), 1635–1666
Linking options:
https://www.mathnet.ru/eng/sm525https://doi.org/10.1070/sm2000v191n11ABEH000525 https://www.mathnet.ru/eng/sm/v191/i11/p47
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Abstract page: | 453 | Russian version PDF: | 219 | English version PDF: | 4 | References: | 51 | First page: | 1 |
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