Parametrized topological complexity of poset-stratified spaces.

Abstract

In this paper, parametrized motion planning algorithms for a fiberwise space $X\to P$ over a poset P are studied. Such an algorithm assigns paths in a space X decomposed into subspaces with the index set P, that do not cross the boundaries of the separated regions. We compute the parametrized topological complexity of $X\to P$ , which is one less than the minimal number of local parametrized motion planning algorithms used for designing non-cross-border robot motions in X.