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seen Sep 1 at 6:11

I am a great fan of the Atiyah-Singer Index Theorem:

Let $ P $ be an elliptic partial differential operator of order $ d $ on a closed smooth even-dimensional manifold $ M $. Let $ [{\sigma_{d}}(P)] \in K(T M) $ be the symbol class of $ P $. Then $$ \text{Index}(P) = \int_{T^{*} M} \text{ch}([{\sigma_{d}}(P)]) \smile \text{Td}(T M \otimes \mathbb{C}). $$


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