Editing Todd class (section)

==Properties of the Todd class==
The Todd class is multiplicative: 
::<math>\operatorname{td}(E\oplus F) = \operatorname{td}(E)\cdot \operatorname{td}(F).</math>

Let <math>\xi \in H^2({\mathbb C} P^n)</math> be the fundamental class of the hyperplane section.
From multiplicativity and the Euler exact sequence for the tangent bundle of <math> {\mathbb C} P^n</math>
:: <math> 0 \to  {\mathcal O} \to {\mathcal O}(1)^{n+1}   \to T {\mathbb C} P^n \to 0,</math>
one obtains
<ref>[http://math.stanford.edu/~vakil/245/245class18.pdf Intersection  Theory Class 18], by [[Ravi Vakil]]</ref> 
:: <math> \operatorname{td}(T {\mathbb C}P^n) =  \left( \dfrac{\xi}{1-e^{-\xi}} \right)^{n+1}.</math>