Multisections and stable commutator lengths, I

Mitsumatsu and Vogt asked whether there is a bound on the
self-intersection numbers of multisections in surface bundles over
surfaces in terms of the genus of fibre and base. We will discuss a
natural stable analogue of this question, whose solution involves the
computation of stable commutator lengths in certain stable groups and has
non-trivial implications for their original question.