15 citations · 73 across the 18 of their papers we have counts for
4 papers · 1 filter
Symmetric Motion Planning
Michael Farber, Mark Grant
In this paper we study symmetric motion planning algorithms, i.e. such that the motion from one state A to another B, prescribed by the algorithm, is the time reverse of the motion…
Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles
Michael Farber, Mark Grant, Sergey Yuzvinsky
We study motion planning algorithms for collision free control of multiple objects in the presence of moving obstacles. We compute the topological complexity of algorithms solving…
Homology of planar polygon spaces
Michael Farber, Dirk Schuetz
In this paper we study topology of the variety of closed planar polygons with given side lengths. We describe the Betti numbers of the moduli spaces as functions of the length vect…
Novikov-Betti numbers and the fundamental group
Michael Farber, Dirk Schuetz
We prove that nonvanishing of the first Novikov-Betti number implies that the fundamental group contains a nonabelian free subgroup.