Abstract

We survey the 1953 basic work of Hirzebruch on Chern classes for the Riemann-Roch theorem and Pontrjagin classes for the signature theorem. Recent applications are considered.

Today 23 July 2009 a former student in Iran, Majid Hadian, just came into my office at the MPI in Bonn and said that he had just learned the Pontjagin class of any oriented 4-manifold is divisible by 3. He was very pleased with his topology course. This is an example of an application of the signature theorem where number theory considerations in the form of divisibility questions come into topology.



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