The Eisenbud–Levine–Khimshiashvili signature formula

I learned last week of a really cool result, published when I was a first-year undergraduate, that I had not been aware of before.  Maybe everyone knew it except me, but it is so neat I’m going to write about it anyway.

To set the scene, think about the Hopf index theorem for vector fields on a (compact, oriented)  $$n$$-manifold.  Continue reading

Wodzicki-Chern Classes

So I took a look today at this new paper on the arXiv, by Steve Rosenberg and collaborators, that considers bundles (typically over infinite-dimensional manifolds) whose structural group is a subgroup of the invertible pseudodifferential operators of order $$\le 0$$ (on some other manifold).