15 citations · 60 across the 12 of their papers we have counts for
4 papers · 1 filter
Topology of randon linkages
Michael Farber
Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters -- the lengths of the bars of the linkage. Motiva…
On the conjecture of Kevin Walker
Michael Farber, Jean-Claude Hausmann, Dirk Schuetz
In 1985 Kevin Walker in his study of topology of polygon spaces raised an interesting conjecture in the spirit of the well-known question "Can you hear the shape of a drum?" of Mar…
Robot motion planning, weights of cohomology classes, and cohomology operations
Michael Farber, Mark Grant
The complexity of algorithms solving the motion planning problem is measured by a homotopy invariant TC(X) of the configuration space X of the system. Previously known lower bounds…
Betti numbers of random manifolds
Michael Farber, Thomas Kappeler
We study mathematical expectations of Betti numbers of configuration spaces of planar linkages, viewing the lengths of the bars of the linkage as random variables. Our main result…