Appears in collection : 2024 - T2 - WS1 - Low dimensional actions

We classify all closed manifolds admitting a smooth locally free action by a higher rank split simple Lie group with codimension 1 orbits. Namely, if a closed manifold M admits such an action by a Lie group G as above, M is finitely and equivariantly covered by G/Gamma x S^1, for some cocompact lattice Gamma of G, where G acts by left translations on the first factor, and trivially on S^1. This result is in the spirit of the Zimmer program. We will focus on the case G = SL(3,R) for the talk.