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

Abstract

We study the topology of moduli spaces of closed linkages in ℝd depending on a length vector ℓ ∈ ℝn. 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.