Geometry & Topology seminar

Romina Arroyo, McMaster University

“Homogeneous Ricci solitons and the Alekseevskii conjecture in low dimensions”

One of the most important open problems on Einstein homogeneous manifolds is ”Alekseevskii’s conjecture”. This conjecture says that any homogeneous Einstein space of negative scalar curvature is diffeomorphic to a Euclidean space. Due to recent results of Lafuente - Lauret and Jablonski, this conjecture is equivalent to the analogous statement for expanding algebraic solitons, which we call ”Generalized Alekseevskii’s conjecture”.

The aim of this talk is to study the classification of expanding algebraic solitons in low dimensions and use these results to check that the Generalized Alekseevskii conjecture holds in these dimensions. We also present our work in progress: the Alekseevskii conjecture holds up to dimension 8 (excluding the case of semisimple Lie groups), and up to dimension 10 when the transitive group is not semisimple. This talk is based on joint works with Ramiro Lafuente.