The Height of a Class in the Cohomology Ring of Polygon Spaces

الملخص EN

Let M-n,r be the configuration space of planar n-gons having side lengths 1,…,1 and r modulo isometry group.

For generic r, the cohomology ring H*(M-n,r;ℤ2) has a form H*(M-n,r;ℤ2)=ℤ2[R(n,r),V1,…,Vn-1]/ℐn,r, where R(n,r) is the first Stiefel-Whitney class of a certain regular 2-cover π:Mn,r⟶M-n,r and the ideal ℐn,r is in general big.

For generic r, we determine the number h(n,r) such that R(n,r)h(n,r)≠0 but R(n,r)h(n,r)+1=0.