Hopf Invariants for sectional category with applications to topological robotics
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 in the study of Farber's topological complexity for 2-cell complexes, as well as in the construction of a counter-example to the analogue for topological complexity of Ganea's conjecture on Lusternik-Schnirelmann category.
Cite
@article{arxiv.1405.6891,
title = {Hopf Invariants for sectional category with applications to topological robotics},
author = {Jesús González and Mark Grant and Lucile Vandembroucq},
journal= {arXiv preprint arXiv:1405.6891},
year = {2017}
}
Comments
v4: 39 pages, incorporating comments from a referee. v3: 38 pages. Improved exposition and strengthened our results on TC of 2-cell complexes. v2: 36 pages. Completely re-written, with a new co-author and new title. We now calculate TC of many 2-cell complexes in the metastable range, and exhibit a counter-example to the TC analogue of Ganea's conjecture