01 · A life in mathematics
The person behind the work
Sergei Novikov was born in Gorky, now Nizhny Novgorod, in 1938. His early work transformed algebraic and differential topology, including the topological invariance of rational Pontryagin classes. He received the 1970 Fields Medal while working at Moscow State University and the Steklov Mathematical Institute. These appointments are documented in his scientific biography, correcting an inconsistent institution in the IMU retrospective list. Novikov later connected geometry with mathematical physics and integrable systems. His medal-period achievements revealed unexpectedly stable information beneath the choice of a smooth structure.
The contribution, explained
A smooth manifold has a tangent bundle, from which one constructs characteristic classes measuring global geometric twisting. It was not obvious which of these quantities survive when only a homeomorphism, rather than a smooth equivalence, relates two manifolds. Novikov proved that rational Pontryagin classes are topological invariants. The theorem reveals that information initially defined through smooth machinery can be determined by the underlying continuous shape. This connects characteristic classes, topology and manifold classification, while carefully distinguishing rational information from stronger integral or smooth assertions.
Why it matters
Topological invariance of rational Pontryagin classes gave a fundamental constraint on manifold structures and helped reshape the relationship between algebraic topology and differential geometry.