3 jul 2015 -- 09:00
Bielefeld University
Abstract.
A manifold is called rationally elliptic if its rational homotopy groups, form a finite dimensional vector space over $\mathbb{Q}$. In this talk we look at effective actions by tori on rationally elliptic manifolds. In particular, we produce sharp bounds for the dimension of the torus in term of the dimension of $M$, and provide a classification up to rational homotopy equivalence of those manifolds admitting actions of maximal dimension. In particular, we provide further evidence to the conjectured relationship between non-negatively curved and rationally elliptic manifolds.