A trivial exercise in mathematics

Let P(f)=0 be an elliptic system of partial differential equations defined over a closed, smooth, oriented n-dimensional manifold X. then:

Topological index of P = Analytical index of P = (-1)^n <ch(s(P)) . td(T_C X), [X]>

where
n is the dimension of the space
s(P) is the symbol of the system
ch is the Chern character
T_C X is the complexified tangent bundle on X
td is the Todd class
. is the cup product
[X] is the fundamental class of X
<a,b> is the Kronecker pairing

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