Abstract
We prove that a space whose topological complexity equals 1 is homotopy equivalent to some odd-dimensional sphere. We prove a similar result, although not in complete generality, for spaces X whose higher topological complexity TCn (X) is as low as possible, namely n - 1.
| Original language | English |
|---|---|
| Pages (from-to) | 73-81 |
| Number of pages | 9 |
| Journal | Homology, Homotopy and Applications |
| Volume | 15 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2013 |
Keywords
- Lusternik-Schnirelmann category
- topological complexity
- topological robotics
- acyclic space
- co-H-space
- homology sphere