Let $G$ be a compact Lie group and $\pi:P \to M$ a principal $G$-bundle. I would like to understand the geometry of $M$ through $P$ with the $G$-action. I am trying to understand the Hopf bundle ...
The relation between the heat kernel on the principal bundle and the heat kernel on the base manifold
This question is mainly about Section 5.2 of the book "Heat Kernels and Dirac Operators" by Berline, Getzler and Vergne. Let $M$ be a compact Riemannian manifold without boundary and $P\rightarrow M$ ...
In the Atiyah-Singer paper mentioned above, they introduced on p.557 a concept called $H$-structure which is used to describe the Chern character of special elements of $K(TX)$. It is roughly the ...