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arXiv · 1708.03971

Topology of maximally writhed real algebraic knots

Grigory Mikhalkin·Stepan Orevkov
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Abstract

Oleg Viro introduced an invariant of rigid isotopy for real algebraic knots in $RP^3$ 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.

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Grigory Mikhalkin, Stepan Orevkov. 2017-08-13. Topology of maximally writhed real algebraic knots. https://doi.org/10.1134/s106456241801009x

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