When studying the Atiyah-Singer index theorem one usually sees four main examples. Atiyah-Singer operator: Its topological index is the \(\hat{A}\)-genus and its analytical index can be related to scalar curvature. This shows that the \(\hat{A}\)-genus of a manifold is an obstruction to the existence of a Riemannian metric of positive scalar curvature on it. Signature … Continue reading "K-homology class of the Euler characteristic operator"

This is basically a repost of this blog post by John Carlos Baez: link. I wanted to share it with you since I find the result unexpectedly interesting. The Law of Excluded Middle states that for any statement P we have that either P or not P is true. Almost all of us work under … Continue reading "The Probability of the Law of Excluded Middle"