Joins of DGA modules and sectional category

Abstract

a lower bound of the sectional category of a fibration p which can be calculated from any Sullivan model of p and which is closer to the sectional category of p than the classical cohomological lower bound given by the nilpotency of the kernel of p W H .BIQ/!H .EIQ/. In the special case of the evaluation fibration X I !X X we obtain a computable lower bound of Farber’s topological complexity TC.X/. We show that the difference between this lower bound and the classical cohomological lower bound can be arbitrarily large. 55M30; 55P62