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

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We study the topology of moduli spaces of closed linkages in ᵈ depending on a length vector ℓ∈ 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 Poincare polynomial in terms of combinatorial information encoded in the length vector.