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Sbornik: Mathematics, 2003, Volume 194, Issue 9, Pages 1301–1330
DOI: https://doi.org/10.1070/SM2003v194n09ABEH000766 (Mi sm766) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Vassiliev invariants classify plane curves and doodles

A. B. Merkov

Institute of Systems Analysis, Russian Academy of Sciences
English version PDF (357 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM2003v194n09ABEH000766
Abstract: An ornament is a system of oriented closed curves in a plane or some other 2-surface no three of which intersect at one point. Similarly, a doodle is a collection of oriented closed curves without triple points or degenerations. Homotopy invariants of ornaments and doodles are natural analogues of homotopy and isotopy invariants of links, respectively. The Vassiliev theory of finite-order invariants of ornaments and the constructions of certain series of such invariants can be applied to doodles. It is proved that these finite-order invariants classify doodles. Similar finite-order invariants of connected oriented closed curves classify doodles up to an isotopy of the ambient plane.
Received: 26.12.2002
Russian version:
Matematicheskii Sbornik, 2003, Volume 194, Number 9, Pages 31–62
DOI: https://doi.org/10.4213/sm766
Bibliographic databases:
UDC: 515.1
MSC: 57M25, 57M27, 57M99
Language: English
Original paper language: Russian
Citation: A. B. Merkov, “Vassiliev invariants classify plane curves and doodles”, Mat. Sb., 194:9 (2003), 31–62; Sb. Math., 194:9 (2003), 1301–1330
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:292
    English version PDF:12
    References:58
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