# Riemannian Topology Meeting

8-9 November 2018
University of Fribourg, Switzerland
Europe/Berlin timezone

## A rigidity theorem for the action of the diffeomorphism group on spaces of psc metrics

8 Nov 2018, 09:20
50m
University of Fribourg, Switzerland

Johannes Ebert

### Description

For a closed, simply connected $d$-dimensional manifold spin $M$, we study the action of the (spin) diffeomorphism group of $M$ on the space $\mathcal{R}^+ (M)$ of psc metrics on $M$. Our main result is that the homotopy class of the map $f^*: \mathcal{R}^+ (M) \to \mathcal{R}^+ (M)$ only depends on the cobordism class in $\Omega^{\mathrm{Spin}}_{d+1}$ of the mapping torus of $f$. When properly formulated, the same result is true for manifolds with nontrivial fundamental group.

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