Topology of Maximally Writhed Real Algebraic Knots¹

G. B. Mikhalkin^a^,* and S. Yu. Orevkov^b^,^c^,^d^, **

^aUniversité de Genève, Section de Mathématiques, Battelle Villa, Carouge, 1227 Suisse

^bSteklov Mathematical Institute, Moscow, 119991 Russia

^cIMT, Université Paul Sabatier, Toulouse, 31062 France

^dNational Research University Higher School of Economics, Russian Academy of Sciences, Moscow, 119048 Russia

Correspondence to: *e-mail: grigory.mikhalkin@unige.ch
Correspondence to: **e-mail: orevko@math.ups-tlse.fr

¹The article was translated by the authors.

Received 15 August, 2017

Abstract—Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots in $\mathbb{R}{{\mathbb{P}}^{3}}$ 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.

DOI: 10.1134/S106456241801009X

Topology of Maximally Writhed Real Algebraic Knots1

Topology of Maximally Writhed Real Algebraic Knots¹