Licentiate Seminar: Floor-crossing and Legendrian Clasp Move

Opponent is Paolo Ghiggini, Université Grenoble Alpes

Abstract: We investigate the effect of the clasp move of Legendrian submanifolds of dimension 2 and higher on the moduli spaces of pseudo-holomorphic curves that contribute to the differential of the Chekanov-Eliashberg algebra. As an application, we compute the Chekanov-Eliashberg algebra differential of twist spheres Λ_k of dimension greater than 1. Moreover, we construct an infinite family of Legendrians T(Λ, k) from any horizontally displaceable Legendrian Λ in P×R, such that the Chekanov-Eliashberg algebra of T(Λ,k) admits an augmentation, while T(Λ,k) has no exact embedded Lagrangian filling of vanishing Maslov class in the symplectization of P×R for sufficiently large k.

The full thesis is available in the university’s publication database DiVA.