ON THE GROMOV WIDTH OF POLYGON SPACES

For generic r = (r1, aEuro broken vertical bar , rn) a the space a"(3)(r) of n-gons in a"e(3) with edges of lengths r is a smooth, symplectic manifold. We investigate its Gromov width and prove that the expression 2 pi min {2r (j) , (a (i not equal j) r (i) ) - r (i) |j = 1, aEuro broken vertical bar , n} is the Gromov width of all (smooth) 5-gon spaces and of 6-gon spaces, under some condition on r a . The same formula constitutes a lower bound for all (smooth) spaces of 6-gons. Moreover, we prove that the Gromov width of a"(3)(r) is given by the above expression when a"(3)(r) is symplectomorphic to a",a"(TM) (n - 3), for any n ae 4.