Positive scalar curvature and higher-dimensional families of Seiberg-Witten equations
arXiv:1707.08974 · doi:10.1112/topo.12117
Abstract
We introduce an invariant of tuples of commutative diffeomorphisms on a 4-manifold using families of Seiberg-Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1-parameter families of Seiberg-Witten equations. Our invariant yields an application to the homotopy groups of the space of positive scalar curvature metrics on a 4-manifold. We also study the extension problem for families of 4-manifolds using our invariant.
22 pages, accepted for publication by the Journal of Topology