91 citations · 276 across the 48 of their papers we have counts for
7 papers · 1 filter
Analog category and complexity
Ben Knudsen, Shmuel Weinberger
We study probabilistic variants of the Lusternik--Schnirelmann category and topological complexity, which bound the classical invariants from below. We present a number of computat…
Parametrized topological complexity of sphere bundles
Michael Farber, Shmuel Weinberger
Parametrized motion planning algorithms have high degree of flexibility and universality, they can work under a variety of external conditions, which are viewed as parameters and f…
Fixed Point Sets and the Fundamental Group II: Euler Characteristics
Sylvain Cappell, Shmuel Weinberger, Min Yan
For a group of not prime power order, Oliver showed that the obstruction for a finite CW-complex to be the fixed point set of a contractible finite -CW-complex is the Eu…
Fixed Point Sets and the Fundamental Group I: Semi-free Actions on G-CW-Complexes
Sylvain Cappell, Shmuel Weinberger, Min Yan
Smith theory says that the fixed point of a semi-free action of a group on a contractible space is ${\bb Z}_p$-acyclic for any prime factor of . Jones proved the convers…
Parametrized topological complexity of collision-free motion planning in the plane
Daniel C. Cohen, Michael Farber, Shmuel Weinberger
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as…
Topology of parametrised motion planning algorithms
Daniel C. Cohen, Michael Farber, Shmuel Weinberger
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the para…