Published online by Cambridge University Press: 17 April 2009
Let Mn be the “polygon space” introduced by Kirwan and Klyachko. In this paper, we give new results on the topology of Mn for odd n. We determine πq(Mn) (q ≤ n − 3). Then we describe Mn in the oriented cobordism ring . We also give new and elementary proofs of the result on the ring structure of H*(Mn/Sn; Q), where Sn denotes the symmetric group acting naturally on Mn.