Vladimir Abramovich Rokhlin (

Russian Russian(s) may refer to: *Russians (), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *A citizen of Russia *Russian language, the most widely spoken of the Slavic languages *''The Russians'', a b ...

: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was a

Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

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, mathematical structure, structure, space, Mathematica ...

, 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 invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

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 magnitude (mathematics), magnitude, mass, and probability of events. These seemingl ...

probability theory Probability theory or probability calculus 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 expre ...

ergodic theory Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behav ...

and entropy theory.

Life

Vladimir Abramovich Rokhlin was born in

Baku Baku (, ; ) is the Capital city, capital and List of cities in Azerbaijan, largest city of Azerbaijan, as well as the largest city on the Caspian Sea and in the Caucasus region. Baku is below sea level, which makes it the List of capital ci ...

Azerbaijan Azerbaijan, officially the Republic of Azerbaijan, is a Boundaries between the continents, transcontinental and landlocked country at the boundary of West Asia and Eastern Europe. It is a part of the South Caucasus region and is bounded by ...

, 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 The Great Purge, or the Great Terror (), also known as the Year of '37 () and the Yezhovshchina ( , ), was a political purge in the Soviet Union that took place from 1936 to 1938. After the Assassination of Sergei Kirov, assassination of ...

, and executed in 1941). Vladimir Rokhlin entered

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

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 ...

. In 1940 he graduated from the MSU Faculty of Mechanics and Mathematics.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 or captivity in a prison or physical restraint. The term usually applies to one serving a Sentence (law), se ...

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 Soviet ...

and

Lev Pontryagin Lev Semyonovich Pontryagin (, also written Pontriagin or Pontrjagin, first name sometimes anglicized as Leon) (3 September 1908 – 3 May 1988) was a Soviet mathematician. Completely blind from the age of 14, he made major discoveries in a numbe ...

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

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

, after which he returned to mathematics. At Pontryagin's suggestion, he joined

Steklov Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...

as Pontryagin's official research assistant. In the 1950s, during the

anti-cosmopolitan campaign The anti-cosmopolitan campaign (, ) was an anti-Western campaign in the Soviet Union which began in late 1948 and has been widely described as a thinly disguised antisemitic purge. A large number of Jews were persecuted as Zionists or rootless co ...

, he was forced to resign from Steklov Institute of Mathematics and leave the capital. In 1952-1955 he worked in higher education institutions of

Arkhangelsk Arkhangelsk (, ) is a types of inhabited localities in Russia, city and the administrative center of Arkhangelsk Oblast, Russia. It lies on both banks of the Northern Dvina near its mouth into the White Sea. The city spreads for over along the ...

. In 1955 Rokhlin and his family managed to move closer to Moscow, to academic institutes. Since September 1955 he has been a professor of the Department of Mathematical Analysis at the

Ivanovo State University Ivanovo State University () or IvSU () is in Ivanovo, about 300 km east of Moscow, Russia. The university was founded in 1918; before 1974, it was called Ivanovo State Pedagogical Institute. IvSU has accreditation and a license from the Russia ...

, since 1957 he has been a professor of the Department of Mathematics at the Kolomna Pedagogical Institute. In 1959 Rokhlin joined

Leningrad State University Saint Petersburg State University (SPBGU; ) is a public research university in Saint Petersburg, Russia, and one of the oldest and most prestigious universities in Russia. Founded in 1724 by a decree of Peter the Great, the university from the be ...

as a faculty member. He died in 1984 in

Leningrad Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

. His students include Viatcheslav Kharlamov, Yakov Eliashberg, Mikhail Gromov, Nikolai V. Ivanov,

Anatoly Vershik Anatoly Moiseevich Vershik (; 28 December 1933 – 14 February 2024) was a Soviet and Russian mathematician. He is most famous for his joint work with Sergei V. Kerov on representations of infinite symmetric groups and applications to the lon ...

and Oleg Viro.

Work

Rokhlin's contributions to

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

include

Rokhlin's theorem In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, orientable, closed 4-manifold ''M'' has a spin structure (or, equivalently, the second Stiefel–Whitney class w_2(M) vanishes), then the signature of ...

, a result of 1952 on the

signature A signature (; from , "to sign") is a 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 intent. Signatures are often, but not always, Handwriting, handwritt ...

of . 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 to which the bundle is "twisted" and whether it possesses sections. Characterist ...

es,

homotopy theory In mathematics, homotopy theory is a systematic study of situations in which Map (mathematics), maps can come with homotopy, homotopies between them. It originated as a topic in algebraic topology, but nowadays is learned as an independent discipli ...

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 Standard may refer to: Symbols * Colours, standards and guidons, kinds of military signs * Standard (emblem), a type of a large symbol or emblem used for identification Norms, conventions or requirements * Standard (metrology), an object t ...

, 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 university, private Ivy League research university in New Haven, Connecticut, United States. Founded in 1701, Yale is the List of Colonial Colleges, third-oldest institution of higher education in the United Stat ...

. 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