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 \△.