# Tagged Questions

**7**

votes

**0**answers

79 views

### Euler number of the complex of basic forms

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 ...

**2**

votes

**1**answer

217 views

### 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 $P\rightarrow M$ ...

**2**

votes

**1**answer

315 views

### Index of elliptic operators III: H-structure invariant under a group G

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 ...