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- Title
Hopf invariants for sectional category with applications to topological robotics.
- Authors
González, Jesús; Grant, Mark; Vandembroucq, Lucile
- 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.
- Subjects
ROBOTICS; LOGICAL prediction; CONSTRUCTION; MANUFACTURED products; INVARIANTS (Mathematics)
- Publication
Quarterly Journal of Mathematics, 2019, Vol 70, Issue 4, p1209
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/haz019