Abstract
We give new lower bounds for the (higher) topological complexity of a space, in terms of the LusternikSchnirelmann category of a certain auxiliary space. We also give new lower bounds for the rational topological complexity of a space, and more generally for the rational sectional category of a map, in terms of the rational category of a certain auxiliary space. We use our results to deduce consequences for the global (rational) homotopy structure of simply connected, hyperbolic finite complexes.
| Original language | English |
|---|---|
| Pages (from-to) | 1643-1666 |
| Number of pages | 24 |
| Journal | Algebraic & Geometric Topology |
| Volume | 15 |
| Issue number | 3 |
| Early online date | 19 Jun 2015 |
| DOIs | |
| Publication status | Published - 19 Jun 2015 |
Keywords
- Lusternik–Schnirelmann category
- sectional category
- topological complexity
- topological robotics
- sectioned fibration
- connective cover
- Avramov–Félix conjecture