Hopf Invariants for sectional category with applications to topological\n robotics

Abstract

We develop a theory of generalized Hopf invariants in the setting of\nsectional category. In particular we show how Hopf invariants for a product of\nfibrations can be identified as shuffle joins of Hopf invariants for the\nfactors. Our results are applied in the study of Farber's topological\ncomplexity for 2-cell complexes, as well as in the construction of a\ncounter-example to the analogue for topological complexity of Ganea's\nconjecture on Lusternik-Schnirelmann category.\n