The Alekseevskii conjecture in low dimensions.

LAFUENTE, RAMIRO A.; ARROYO, ROMINA M.

Congreso; International Congress of Mathematician; 2018

One of the most important open problems on Einstein homogeneous manifolds is theAlekseevskii conjecture. This conjecture says that any connected homogeneous Einstein space of negative scalar curvature is diffeomorphic to a Euclidean space.The aim of this talk is to show that the Alekseevskii conjecture holds up to dimension 8 (excluding 5 possible exceptions), and also in dimensions 9 and 10 provided the transitive group is not semisimple.This talk is based in a joint work with Ramiro Lafuente.