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 2-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.
|Number of pages||43|
|Journal||Quarterly Journal of Mathematics|
|Early online date||15 Jul 2019|
|Publication status||Published - Dec 2019|
- Sectional category
- topological complexity
- generalized Hopf invariants
- two-cell complexes
- Ganea conjecture
- join and shuffle maps
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- School of Natural & Computing Sciences, Mathematical Science - Senior Lecturer