Speaker
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.
