Vladimir Abramovich Rokhlin

Vladimir Abramovich Rokhlin (Russian: Владимир Абрамович Рохлин, English transliteration Vladimir Abramovich Rokhlin, born August 23, 1919 in Baku, † December 3, 1984 in Leningrad) was a Russian mathematician who worked on topology, ergodic theory and real algebraic geometry.

Life

Rochlin came from a Jewish family and studied from 1935 at the Lomonosov University in Moscow with Andrei Kolmogorov and Lev Semenovich Pontryagin. In 1941 he volunteered for the Red Army and spent several years in German prison camps and then two years in a Russian prison camp. He was only released on the use of his former teacher Pontryagin, who personally appealed to the intelligence chief Beria and Rokhlin then as personal secretary spent ( Pontryagin was blind ), since this would otherwise not receive a residence permit for Moscow. In 1952 he attracted with his four-dimensional manifolds Signaturtheorem for attention. There is a necessary condition for the existence of a spinning structure in a four -manifold: the signature of the sectional shape ( a square shape in the second cohomology group ) must be divided by 16. Rokhlin proved the theorem proved by him from the property of the third stable homotopy groups of spheres to be cyclic with period 24. According to Friedrich Hirzebruch, it follows from the Atiyah-Singer index theorem. Other evidence comes from Michel Kervaire and John Milnor and Michael Freedman and Robion Kirby.

He also worked on characteristic classes, homotopy theory and Kobordismentheorie.

From 1959 he was professor at the University of St. Petersburg ( then Leningrad ). His students include Mikhail Gromov (PhD 1968), Yakov Eliaschberg, Oleg Wiro, Viatcheslav Kharlamov and Anatoli Werschik His son Vladimir Rokhlin is also a well-known mathematician. Rochlins uncle Korney Ivanovich Chukovsky was a Russian author of children's books.