Cabling Families of Legendrian Embeddings

Eduardo Fernández

I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the space of Legendrian embeddings in the standard contact 3-sphere that satisfy an injective h-principle. These components include those containing positive Legendrian torus knots with the maximal Thurston-Bennequin invariant. This work is a collaboration with Hyunki Min.

https://www.ias.edu/video/cabling-families-legendrian-embeddings