15 citations · 43 across the 6 of their papers we have counts for
27 papers
Collision Free Motion Planning on Graphs
Michael Farber
A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithm…
L^2 torsion without the determinant class condition and extended L^2 cohomology
M. Braverman, A. Carey, M. Farber +1
We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatoria…
Smooth Lyapunov 1-forms
M. Farber, T. Kappeler, J. Latschev +1
We find conditions which guarantee that a given flow on a closed smooth manifold admits a smooth Lyapunov one-form lying in a prescribed de Rham cohomology class. These conditions…
Topological Robotics: Subspace Arrangements and Collision Free Motion Planning
Michael Farber, Sergey Yuzvinsky
We study an elementary problem of the topological robotics: collective motion of a set of distinct particles which one has to move from an initial configuration to a final conf…
Topological robotics: motion planning in projective spaces
Michael Farber, Serge Tabachnikov, Sergey Yuzvinsky
We study an elementary problem of topological robotics: rotation of a line, which is fixed by a revolving joint at a base point: one wants to bring the line from its initial positi…
Instabilities of Robot Motion
Michael Farber
Instabilities of robot motion are caused by topological reasons. In this paper we find a relation between the topological properties of a configuration space (the structure of its…