# Mathematical Field Notes

## Gromoll filtration

In my latest preprint with Georgios Dimitroglou Rizell, we use the topology of diffeomorphism groups of high-dimensional spheres to produce interesting examples of nontrivial topology in symplectomorphism groups of cotangent bundles. Until we started thinking about this, I didn’t know much about the higher homotopy groups of $Diff(S^n)$ so here is some interesting stuff I learned while we were writing this paper.