## Chern-weil Theory in Odd Dimension

In the previous section, we discussed the theory of even dimensional characteristic forms and classes. i.e.
Let $M$ be a smooth closed manifold and $E$ be a vector bundle with a connection $\nabla^E$. We constructed a serial closed form
$\tr\left[f\left(\frac{\sqrt{-1}}{2\pi}R^E \right) \right] \in \Omega^{even}(M),$where $f$ is a power series in one variable. Continue Reading