[math/0603018] On the space of metrics with invertible Dirac operator

[math/0603018] On the space of metrics with invertible Dirac operator

This paper by Mattias Dahl shows that several geometric constructions, eg codim-3 surgery, which one knows how to do in the category of positive scalar curvature manifolds, can in fact be done in the category of spin manifolds with invertible Dirac operator.