Daniel Alvarez-Gavela

We introduce an invariant of Legendrian submanifolds in 1-jet spaces built out of the Turaev torsion of generating families. As an application we exhibit pairs of Legendrian submanifolds in the 1-jet space of any closed orientable surface which are formally isotopic, cannot be distinguished by any natural Legendrian invariant, yet are not Legendrian isotopic. These examples are distinguished by their Legendrian Turaev torsion, which we compute by expressing it in terms of a certain monodromy in the K_3 picture of handle slides. Joint work with K. Igusa.