Short survey on the existence of slices for the space of Riemannian metrics

Abstract

We review the well-known slice theorem of Ebin for the action of the diffeomorphism group on the space of Riemannian metrics of a closed manifold. We present advances in the study of the spaces of Riemannian metrics, and produce a more concise proof for the existence of slices.

21 pages; added references [DR19] and [Kan05]; corrected typos; added propositions 2.2 and 4.6, remarks 2.6, 2.18 and 2.22; to appear in the Proceedings of the IV Meeting of Mexican Mathematicians Abroad 2018