Advertisement

Doklady Mathematics

, Volume 97, Issue 1, pp 28–31 | Cite as

Topology of Maximally Writhed Real Algebraic Knots

  • G. B. Mikhalkin
  • S. Yu. Orevkov
Mathematics
  • 22 Downloads

Abstract

Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots in ℝℙ3 which can be viewed as a first order Vassiliev invariant. In this paper we look at real algebraic knots of degree d with the maximal possible value of this invariant. We show that for a given d all such knots are topologically isotopic and explicitly identify their knot type.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Björklund, J. Knot Theory Ramifications 20 (9), 1285–1309 (2011).MathSciNetCrossRefGoogle Scholar
  2. 2.
    G. Mikhalkin and S. Orevkov, J. Knot Theory Ramifications 25, 1642010 (2016).MathSciNetCrossRefGoogle Scholar
  3. 3.
    K. Murasugi, Trans. Am. Math. Soc. 326 (1), 237–260 (1991).CrossRefGoogle Scholar
  4. 4.
    O. Viro, “Encomplexing the writhe,” in Topology, Ergodic Theory, Real Algebraic Geometry: Rokhlin's Memorial, Ed. by V. Turaev and A. Vershik (Am. Math. Soc., Providence, RI, 2001), pp. 241–256.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Université de Genève, Section de MathématiquesBattelle VillaCarougeSuisse
  2. 2.Steklov Mathematical InstituteMoscowRussia
  3. 3.IMTUniversité Paul SabatierToulouseFrance
  4. 4.National Research University Higher School of EconomicsRussian Academy of SciencesMoscowRussia

Personalised recommendations