We show that a quasipositive surface with disconnected boundary induces map between the knot Floer homology groups of its components preserving transverse invariant. As an application, we this invariant can be used to obstruct decomposable Lagrangian cobordisms arbitrary genus within Weinstein cobordisms. The construction our maps rely on comultiplicativity Along way, also recover various natur...

In this paper we introduce the class of decomposable discrete sets and give a polynomial algorithm for reconstructing discrete sets of this class from four projections. It is also shown that the class of decomposable discrete sets is more general than the class S ′ 8 of hv-convex 8but not 4-connected discrete sets which was studied in [3]. As a consequence we also get that the reconstruction fr...