After Gromov' foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold (M,\omega) is a symplectic invariant that measures, roughly speaking, the size of the biggest ball we can symplectically embed in (M,\omega). I will discuss tecniques to compute the Gromov width of a special family of symplectic manifolds, the moduli spaces of polygons in R3 with edges of lengths (r1,...,rn). Under some genericity assumptions on lengths ri, the polygon space is a symplectic manifold. In fact it is a symplectic reduction of Grassmannian manifold of 2-planes in Cn . After introducing this family of manifolds we will concentrate on the spaces of 5-gons and calculate for their Gromov width.This is joint work with Milena Pabiniak, IST Lisbon.
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