# On the topological complexity of manifolds with abelian fundamental group

### online | 2021-01-11 | 15:00

Lucile Vandembroucq

Centro de Matemática da Universidade do Minho

The topological complexity is a numerical homotopy invariant introduced by M. Farber in his topological approach to the motion planning problem. We will give sufficient conditions for the topological complexity of a closed manifold $M$ with abelian fundamental group to be nonmaximal, that is to satisfy $TC(M)<2\mathrm{dim}(M)$. This generalizes for manifolds some results of A. Costa and M. Farber on the topological complexity of spaces with small fundamental group. We will also see through examples that our conditions are sharp.  This is a joint work with Daniel Cohen.