On the Gromov width of polygon spaces

On the Gromov width of polygon spaces - Alessia Mandini

Alessia Mandini
University of Pavia
October 31, 2014
After Gromov's 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 techniques to compute the Gromov width of a special family of symplectic manifolds, the moduli spaces of polygons in \(\mathbb{R}^3\) with edges of lengths \((r_1,\ldots, r_n)\). Under some genericity assumptions on lengths \(r_i\), the polygon space is a symplectic manifold. After introducing this family of manifolds, I will concentrate on the spaces of 5-gons and calculate their Gromov width.