Conformal geometry of knots

(joint work with R. Langevin (Université de Bourgogne)

I will introduce the “infinitesimal cross ratio”, which is a conformally invariant complex valued 2-form on K × K \△, where K is a knot. I will show that it can express the “energy of knots”, and also give the meanings of its real and imaginary parts using the symplectic form and the semi-Riemannian structure of S³ × S³ \△. (PDF file)