Cancellation properties of exotic 4-dimensional positive scalar curvature metrics

10.07.2025, 16:15  –  Raum 1.22
Forschungsseminar Differentialgeometrie

Johannes Ebert (Münster)

It is well-known that 4-dimensional smooth topology offers many exotic phenomena, typically detected by means of gauge theory, and it is also well-known
that these exoticities are very unstable when suitably stabilized (e.g. by taking products or connected sums with copies of \(S^2 \times S^2\) ).
We show that a similar principle applies to exotic phenomena related to positive scalar curvature metrics on 4-manifolds.
In particular, we prove that Ruberman's classical examples of concordant but not isotopic metrics of positive scalar curvature on certain 4-manifolds all become isotopic after
taking product with any closed N of positive dimension. The proof relies on rigidity theorems for the action of diffeomorphism groups on spaces of metrics of positive scalar
curvature for manifolds of dimension \(\geq 5\) and some bordism--theoretic calculations.