The cobordism ring
In this chapter all manifolds are compact, orientable and differentiable of class C∞. Several results from the cobordism theory of Thom  are stated. They are used to express the index of a manifold M4 k as a polynomial in the Pontrjagin classes of MM4 k (Theorem 8.2.2). This result is needed in 19.5. to provide and essential step in the proof of the Riemann-Roch theorem.
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