A relative Seidel morphism and the Albers map

Abstract

In this note, we introduce a relative (or Lagrangian) version of the Seidel homomorphism that assigns to each homotopy class of paths in Ham(M), starting at the identity and ending on the subgroup that preserves a given Lagrangian submanifold L, an element in the Floer homology of L. We show that these elements are related to the absolute Seidel elements by the Albers map. We also study for later use, the effect of reversing the signs of the symplectic structure as well as the orientations of the generators and of the operations on the Floer homologies.