Characteristic Number Associated to Mass Linear Pairs

Abstract EN

Let Δ be a Delzant polytope in ℝn and b∈ℤn.

Let E denote the symplectic fibration over S2 determined by the pair (Δ,b).

Under certain hypotheses, we prove the equivalence between the fact that (Δ,b) is a mass linear pair (McDuff and Tolman, 2010) and the vanishing of a characteristic number of E.

Denoting by Ham(MΔ), the Hamiltonian group of the symplectic manifold defined by Δ, we determine loops in Ham(MΔ) that define infinite cyclic subgroups in π1(Ham(MΔ)) when Δ satisfies any of the following conditions: (i) it is the trapezium associated with a Hirzebruch sur-face, (ii) it is a Δp bundle over Δ1, and (iii) Δ is the truncated simplex associated with the one point blowup of ℂPn.