Sergei Petrovich Novikov

Sergei Petrovich Novikov (b. 20 March 1938) is a Russian mathematician, noted for work in both algebraic topology and soliton theory. He was born in Gorky (now Nizhny Novgorod).

His early work was in cobordism theory, in relative isolation. Amongst other advances he showed how the Adams spectral sequence, a powerful tool for proceeding from homology theory to the calculation of homotopy groups, could be adapted to the new (at that time) cohomology theory typefied by cobordism and K-theory. This required the development of the idea of cohomology operations in the general setting, since the basis of the spectral sequence is the initial data of Ext functors taken with respect to a ring of such operations, generalising the Steenrod algebra. The resulting Adams-Novikov spectral sequence is now a basic tool in stable homotopy theory.

Novikov also carried out important research in geometric topology, and posed the Novikov conjecture. This work was recognised by the award in 1970 of the Fields Medal.

From about 1971 he moved to work in the field of isospectral flows, with connections to the theory of theta functions.

His father was Pyotr Sergeyevich Novikov, who gave the negative solution of the word problem for groups.