Properties of Glued Knots

Abstract

The study of knots and links in the real projective space has been motivated by newlineone of the questions from the famous list of problems given by Hilbert in 1900. A newlinereal rational knot in RP 3 is an embedding of RP 1 and#8594; RP 3 given by homogeneous newlinepolynomials. All knots in RP 3 are isotopic to some real rational knot and therefore newlinehave a real rational representative. The knots which do not intersect the plane newlineat infinity are also called affine knots and correspond to the classical knots in R 3 . newlineHowever, there are very less known results which tell the relationships between newlineclassical knot theoretic properties and real rational knots.