Hopf invariants for sectional category with applications to topological robotics. (15th July 2019)

• Record Type: Journal Article
• Authors: González, Jesús; Grant, Mark; Vandembroucq, Lucile
• Is Part Of: Quarterly journal of mathematics. Volume 70:Part 4(2019)
• Page Start: 1209
• Page End: 1252
• Publication Date: 2019-07-15
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/qmath/haz019
• Languages: English
• ISSNs: 0033-5606

Abstract

Abstract: 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.