  We give a proof of a Conjecture of Walker which states that one can recover
the lengths of the bars of a circular linkage from the cohomology ring of the
configuration space. For a large class of length vectors, this has been shown
by Farber, Hausmann and Schuetz. In the remaining cases, we use Morse theory
and the fundamental group to describe a subring of the cohomology invariant
under graded ring isomorphism. From this subring the conjecture can be derived
by applying a result of Gubeladze on the isomorphism problem of monoidal rings.

Geometric Topology;Algebraic Topology