Starting from the '80, contact topology, i.e. the study of completely non-integrable plane distributions in 3-manifolds, has become more and more prominent in geometric topology. In recent year equivariant geometry has entered the picture, with the study of knots in S^3 being both set-wise fixed by the standard involution on the sphere, i.e. strongy invertible, and being tangent to such plane distribution, i.e. Legendrian.

The aim of this seminar is to present a classification of invariant tight contact structures on R^3 and S^3: this result could open the door to a coarse classification of strongly invertible Legendrian unknots in the 3-space