We answer affirmatively a question posed by Morita on homological stability of surface diffeomorphisms made discrete. In particular, we prove that C∞-diffeomorphisms of surfaces as family of discrete groups exhibit homological stability. We show that the stable homology of C∞-diffeomorphisms of surfaces as discrete groups is the same as homology of certain infinite loop space related to Haefliger’s classifying space of foliations of codimension 2. We use this infinite loop space to obtain new results about (non)triviality of characteristic classes of flat surface bundles and codimension-2 foliations.
ASJC Scopus subject areas
- Geometry and Topology