Topology of random linkages (Q2471688)

The author's linkages are configurations of points \(x_1,x_2,\dots x_n\) in \(E^3\) (or \(E^2\)) with distances between \(x_i\) and \(x_{i+1}\), and \(x_n\) and \(x_1\) fixed. Fixing these \(n\) distances at \((u_1,u_2,\dots u_n) = l\) determines a manifold \(N_l\) of configurations. The author studies the dependence of the moments of the Betti numbers of \(N_l\) on probability measures on \(l\). He finds, for example, that for a ``reasonably ample class'' of such measures, the asymptotic values of the average Betti numbers do not depend on the choice of measure.