On topological complexity of Eilenberg-MacLane spaces

Abstract

We note that, for any natural $k$ and every natural $l$ between $k$ and $2k$, there exists a group $\pi$ with $\cat K(π,1)=k$ and $\TC(K(π,1))=l$. Because of this, we can set up a problem of searching of purely group-theoretical description of $\TC(K(π,1))$ as an invariant of $\pi$.

Latex, 2 pages, minor corrections

References in corpus (1)

• On topological complexity and LS-category

Cited by in corpus (2)

• Bredon cohomology and robot motion planning
• Right-angled Artin groups, polyhedral products and the TC-generating function