Homotopy equivalence of spaces of metrics with invertible Dirac operator

Abstract

We prove that for cobordant closed spin manifolds of dimension $n\ge 3$ the associated spaces of metrics with invertible Dirac operator are homotopy equivalent. This is the spinorial counterpart of a similar result on positive scalar curvature of Chernysh/Walsh and generalizes the surgery result of Ammann-Dahl-Humbert on the existence of metrics with invertible Dirac operator under surgery. We also give a relative statement of this homotopy equivalence.

References in corpus (2)

• The topology of positive scalar curvature
• On the homotopy type of the space ${\mathcal{R}}^{+}(M)$