Thorsten Hertl: Concordance and bordism spaces of positive scalar curvature

Understanding global topological properties of spaces of positive scalar curvature metrics has been an active endeavour for several decades. For the construction of non-trivial elements in their homotopy groups, one typically relies on the action of diffeomorphism groups and the surgery action of cobordisms, which works for all classes of at least 5-dimensional manifolds. On the detection side, however, the only invariant available for manifolds of dimension at least 5 is the index-difference, which only exists if the manifold under consideration is spin.
In this talk, I will introduce approximation spaces to the spaces of positive scalar curvature metrics and elucidate how they can be used to study the surgery action on the space of positive scalar curvature metrics. As this approach works for spin and non-spin manifolds alike, I will present new examples that could not be detected before to demonstrate its effectiveness.
This talk is based on an ongoing joint project with Georg Frenck.