Vladimir Abramovich Rokhlin ( Russian: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was a

Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, who made numerous contributions in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

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 simila ...

probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...

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 expr ...

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 an ...

Azerbaijan Azerbaijan (, ; az, Azərbaycan ), officially the Republic of Azerbaijan, , also sometimes officially called the Azerbaijan Republic is a transcontinental country located at the boundary of Eastern Europe and Western Asia. It is a part of th ...

, 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 Korney Ivanovich Chukovsky ( rus, Корне́й Ива́нович Чуко́вский, p=kɐrˈnʲej ɪˈvanəvʲɪtɕ tɕʊˈkofskʲɪj, a=Kornyey Ivanovich Chukovskiy.ru.vorb.oga; 31 March NS 1882 – 28 October 1969) was one of the most p ...

, 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 The Great Purge or the Great Terror (russian: Большой террор), also known as the Year of '37 (russian: 37-й год, translit=Tridtsat sedmoi god, label=none) and the Yezhovshchina ('period of Yezhov'), was Soviet General Secreta ...

, and executed in 1941). Vladimir Rokhlin entered

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

in 1935. His advisor was Abraham Plessner. He volunteered for the army in 1941, leading to four years as a

prisoner A prisoner (also known as an inmate or detainee) is a person who is deprived of liberty against their will. This can be by confinement, captivity, or forcible restraint. The term applies particularly to serving a prison sentence in a prison. ...

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 Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Sovi ...

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 d ...

, he was released in December 1946 and allowed to return to

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

, 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 Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...

. 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, Anatoly Vershik and

Oleg Viro Oleg Yanovich Viro (russian: Олег Янович Виро) (b. 13 May 1948, Leningrad, USSR) is a Russian mathematician in the fields of topology and algebraic geometry, most notably real algebraic geometry, tropical geometry and knot theory. ...

Work

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

signature A signature (; from la, signare, "to sign") is a Handwriting, handwritten (and often Stylization, stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and ...

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 mathematics, a smooth structure on a manifold allows for an unambiguous notion of smooth function. In particular, a ...

s. He also worked in the theory of

characteristic class In mathematics, a characteristic class is a way of associating to each principal bundle of ''X'' a cohomology class of ''X''. The cohomology class measures the extent the bundle is "twisted" and whether it possesses sections. Characteristic classes ...

es,

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 topolo ...

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 d ...

, and in the topology of real algebraic varieties. In

, Rokhlin introduced what are now called Rokhlin partitions. 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 ...

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

Family

His son Vladimir Rokhlin, Jr. is a well-known mathematician and computer scientist at

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the w ...

. Rokhlin's uncle was

, a well-known Russian poet, most famous for his popular children's books.

Notes

References

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External links