In this talk, I will sketch a geometrically flavoured proof of the
Madsen-Weiss theorem based on work by Eliashberg-Galatius-Mishachev.
In order to prove the triviality of appropriate relative bordism groups,
in a first step a variant of the wrinkling theorem shows
that one can reduce to consider fold maps (with additional structure).
In a subsequent step, a geometric version of the Harer stability
theorem is used to get rid of the folds via surgery. I will focus on
this second step.
- Junior Geometry and Topology Seminar