The homology of surface diffeomorphism groups and a question of Morita

TL;DR

This paper addresses Morita's question about secondary characteristic classes for surface bundles and demonstrates a form of Harer stability for surface diffeomorphism groups in low-degree homology.

Contribution

It proves the non-triviality of certain secondary characteristic classes and establishes homological stability results for surface diffeomorphism groups.

Findings

Non-trivial secondary characteristic classes for surface bundles

Harer stability in low-degree homology of surface diffeomorphism groups

Answer to Morita's question

Abstract

We answer a question posed by Morita concerning the non-triviality of certain secondary characteristic classes for surface bundles. In doing so we are naturally led to show that a form of Harer stability holds for surface diffeomorphism groups in homology of small degree.