Vladimir Abramovich Rokhlin ( Russian: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry,

measure theory In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...

, probability theory,

ergodic theory Ergodic theory (Greek: ' "work", ' "way") is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, statistical properties means properties which are expres ...

and entropy theory.

Life

Vladimir Abramovich Rokhlin was born in

Baku Baku (, ; az, Bakı ) is the capital and largest city of Azerbaijan, as well as the largest city on the Caspian Sea and of the Caucasus region. Baku is located below sea level, which makes it the lowest lying national capital in the world a ...

, Azerbaijan, to a wealthy Jewish family. His mother, Henrietta Emmanuilovna Levenson, had studied medicine in France (she died in Baku in 1923, believed to have been killed during civil unrest provoked by an epidemic). His maternal grandmother, Clara Levenson, had been one of the first female doctors in Russia. His maternal grandfather Emmanuil Levenson was a wealthy businessman (he was also the illegitimate father of Korney Chukovsky, who was thus Henrietta's half-brother). Vladimir Rokhlin's father Abram Veniaminovich Rokhlin was a well-known social democrat (he was imprisoned during Stalin's Great Purge, and executed in 1941). Vladimir Rokhlin entered Moscow State University in 1935. His advisor was

Abraham Plessner Abraham Plessner (February 13, 1900 – April 18, 1961) was a Russian mathematician. He was born on February 13, 1900, to a Jewish family in Łódź, which is now in Poland. He studied at secondary school where he was taught in Russian, German, an ...

. He volunteered for the army in 1941, leading to four years as a prisoner of a German war camp. During this time he was able to hide his Jewish origins from the Nazis. Rokhlin was liberated by the Soviet military in January 1945. He then served as a German language translator for the 5th Army of the Belorussian front. In May 1945 he was sent to a Soviet 'verification camp' for former prisoners of war. In January 1946 he was transferred to another camp to determine if he was an "enemy of the Soviet." Rokhlin was cleared in June 1946 but was forced to remain in the camp as a guard. Due to intercession by mathematicians Andrey Kolmogorov and

Lev Pontryagin Lev Semenovich Pontryagin (russian: Лев Семёнович Понтрягин, also written Pontriagin or Pontrjagin) (3 September 1908 – 3 May 1988) was a Soviet mathematician. He was born in Moscow and lost his eyesight completely due ...

, he was released in December 1946 and allowed to return to Moscow, after which he returned to mathematics. In 1959 Rokhlin joined

Leningrad State University Saint Petersburg State University (SPBU; russian: Санкт-Петербургский государственный университет) is a public research university in Saint Petersburg, Russia. Founded in 1724 by a decree of Peter the G ...

as a faculty member. He died in 1984 in Leningrad. His students include Viatcheslav Kharlamov,

Yakov Eliashberg Yakov Matveevich Eliashberg (also Yasha Eliashberg; russian: link=no, Яков Матвеевич Элиашберг; born 11 December 1946) is an American mathematician who was born in Leningrad, USSR. Education and career Eliashberg receiv ...

, Mikhail Gromov,

Nikolai V. Ivanov Nikolai V. Ivanov (russian: Николай Владимирович Иванов, born 1954) is a Russian mathematician who works on topology, geometry and group theory (particularly, modular Oswald Teichmüller, Teichmüller groups). He is a prof ...

Anatoly Vershik Anatoly Moiseevich Vershik (russian: Анато́лий Моисе́евич Ве́ршик; born on 28 December 1933 in Leningrad) is a Soviet and Russian mathematician. He is most famous for his joint work with Sergei V. Kerov on representatio ...

and Oleg Viro.

Work

Rokhlin's contributions to topology include Rokhlin's theorem, a result of 1952 on the signature of

4-manifold In mathematics, a 4-manifold is a 4-dimensional topological manifold. A smooth 4-manifold is a 4-manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different. T ...

s. He also worked in the theory of characteristic classes,

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which maps can come with homotopies between them. It originated as a topic in algebraic topology but nowadays is studied as an independent discipline. Besides algebraic topolog ...

cobordism theory In mathematics, cobordism is a fundamental equivalence relation on the class of compact manifolds of the same dimension, set up using the concept of the boundary (French '' bord'', giving ''cobordism'') of a manifold. Two manifolds of the same dim ...

, and in the topology of real algebraic varieties. In

, Rokhlin introduced what are now called

Rokhlin partition Rokhlin is a Slavic language-influenced Jewish surname of matronymic derivation. It literally means "Rokhl's", where "Rokhl" is a transcription of ''Rochl'', a Yiddish form of the name Rachel (given name), Rachel. Variants include Rohlin, Rochlin ...

s. He introduced the notion of

standard probability space In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin i ...

, and characterised such spaces up to isomorphism mod 0. He also proved the famous

Rokhlin lemma In mathematics, the Rokhlin lemma, or Kakutani–Rokhlin lemma is an important result in ergodic theory. It states that an aperiodic measure preserving dynamical system can be decomposed to an arbitrary high tower of measurable sets and a remainder ...

Family

His son

Vladimir Rokhlin, Jr. Vladimir Rokhlin Jr. (born August 4, 1952) is a mathematician and professor of computer science and mathematics at Yale University. He is the co-inventor with Leslie Greengard of the fast multipole method (FMM) in 1985, recognised as one of the to ...

is a well-known mathematician and computer scientist at Yale University. Rokhlin's uncle was Korney Chukovsky, a well-known Russian poet, most famous for his popular children's books.

Notes

References

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External links