## 42.65 Todd classes

A final class associated to a vector bundle $\mathcal{E}$ of rank $r$ is its *Todd class* $Todd(\mathcal{E})$. In terms of the Chern roots $x_1, \ldots , x_ r$ it is defined as

In terms of the Chern classes $c_ i = c_ i(\mathcal{E})$ we have

We have made the appropriate remarks about denominators in the previous section. It is the case that given an exact sequence

we have

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