Real algebraic knots of low degree

Details Real algebraic knots of low degree Real algebraic knots of low degree

2009-05-26

arxiv.org/abs/0905.4186v2

Mathematics

Geometric Topology

28 pages

Scientific paper

10.1142/S0218216511009248

In this paper we study rational real algebraic knots in $\R P^3$. We show that two real algebraic knots of degree $\leq5$ are rigidly isotopic if and only if their degrees and encomplexed writhes are equal. We also show that any irreducible smooth knot which admits a plane projection with less than or equal to four crossings has a rational parametrization of degree $\leq 6$. Furthermore an explicit construction of rational knots of a given degree with arbitrary encomplexed writhe (subject to natural restrictions) is presented.

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