Atiyah-Singer index: ind(D) = int_M A-hat(M) ch(E); Fredholm-K-theory equality

Atiyah-Singer index theorem framework (Atiyah-Singer 1963 Bull AMS 69, 422; 1968 Ann Math 87, 484; Atiyah-Bott 1968 Ann Math 86, 374). Setup: for a compact closed Riemannian manifold M and an elliptic differential operator D acting on…