We develop a theory of generalized Hopf invariants in the setting of sectional category. In particular, we show how Hopf invariants for a product of fibrations can be identified as shuffle joins of Hopf invariants for the factors. Our results are applied to the study of Farber's topological complexity for two-cell complexes, as well as to the construction of a counterexample to the analogue for topological complexity of Ganea's conjecture on Lusternik-Schnirelmann category.
CITATION STYLE
González, J., Grant, M., & Vandembroucq, L. (2019). Hopf invariants for sectional category with applications to topological robotics. Quarterly Journal of Mathematics, 70(4), 1209–1252. https://doi.org/10.1093/qmath/haz019
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