Thu, October 17, 2024
1:50 pm - 2:50 pm
SM1138
Daniel Ruberman
Brandeis University
Title
Homotopy properties of diffeomorphism groups and spaces of positive scalar curvature on 4-manifolds
Abstract
We show that the higher homotopy groups of the diffeomorphism group of a smooth 4-manifold can have infinitely generated free abelian summands. The same applies to the homology of the Torelli subgroup and of its classifying space. We show that the homotopy groups of the space of positive scalar curvature metrics on a large connected sum of S^2 x S^2's can have infinitely generated free abelian subgroups. This is all joint work with Dave Auckly