Seidel's Representation on the Hamiltonian Group of a Cartesian Product

The Seidel morphism of Cartesian products

“…We deduce that any homotopy class of loops of Hamiltonian diffeomorphisms of one component, with nontrivial image via Seidel's morphism, leads to an injection of the fundamental group of the group of Hamiltonian diffeomorphisms of the other component into the fundamental group of the group of Hamiltonian diffeomorphisms of the product. This result was inspired by and extends results obtained by Pedroza [8]. …”

“…Another noteworthy difference between this note and [8] is the approach to Seidel's morphism which we consider. Pedroza approaches the question via the point of view of Hamiltonian fibrations, while we use the representation approach (in terms of automorphisms of Floer homology).…”

Symplectic manifolds with vanishing action–Maslov homomorphism

“…By studying these constraints on the Seidel element and properties of the quantum homology, we can show that I vanishes for products of projective spaces and the Grassmannian G.2; 4/. Theorem 1.1 is related to results of Pedroza [10] and Leclercq [5]. They showed that, for X 0 and X 00 monotone symplectic manifolds, 0 2 1 .Ham.X 0 //, 00 2 1 .Ham.X 00 //, then S. 0 00 / D S. 0 /˝S.…”

On the Cohomology of Classifying Spaces of Groups of Homeomorphisms

“…Remark 7.2. The fundamental group of the group of Hamiltonian diffeomorphisms of a product symplectic manifold has been recently investigated by Pedroza in [12].…”