Homology of moduli spaces of linkages in high-dimensional Euclidean space

Abstract

We study the topology of moduli spaces of closed linkages in ${ℝ}^d$ depending on a length vector $\ell \in {ℝ}^n$. In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd $d$. In the case $d=5$ we calculate the Poincaré polynomial in terms of combinatorial information encoded in the length vector.