Vladimir Abramovich Rokhlin
Encyclopedia
Vladimir Abramovich Rokhlin (Russian
: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was an influential Soviet mathematician
, who made numerous contributions in algebraic topology
, geometry
, measure theory, probability theory
, ergodic theory
and entropy theory
.
, Azerbaijan
, to a wealthy Russian 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 Rokhin 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
. He volunteered for the army in 1941, leading to four years as a prisoner
of a German war camp, and then two years in a Soviet camp
after the end of the war. He then returned to mathematics.
Since 1959 he was at Leningrad State University, where he was a very influential teacher.
His students include Yakov Eliashberg
, Mikhail Gromov, Anatoly Vershik
and Oleg Viro
.
on the signature
of 4-manifold
s, which was subsequently generalised by Hirzebruch. He also worked in the theory of characteristic classes, homotopy theory and cobordism theory.
In measure theory, Rokhlin introduced what is now called Rokhlin partitions. He introduced the notion of standard probability space
, and characterised such spaces up to isomorphism mod 0.
Rokhlin's uncle was Korney Chukovsky
, a well known Russian
poet, most famous for his popular children's books.
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
: Влади́мир Абра́мович Ро́хлин) (23 August 1919 – 3 December 1984) was an influential Soviet mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, who made numerous contributions in algebraic topology
Algebraic topology
Algebraic topology is a branch of mathematics which 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 up to homotopy equivalence.Although algebraic topology...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, measure theory, probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, ergodic theory
Ergodic theory
Ergodic theory is a branch of mathematics that studies dynamical systems with an invariant measure and related problems. Its initial development was motivated by problems of statistical physics....
and entropy theory
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
.
Life
Vladimir Abramovich Rokhlin was born in BakuBaku
Baku , sometimes spelled as Baki or Bakou, is the capital and largest city of Azerbaijan, as well as the largest city on the Caspian Sea and of the Caucasus region. It is located on the southern shore of the Absheron Peninsula, which projects into the Caspian Sea. The city consists of two principal...
, Azerbaijan
Azerbaijan
Azerbaijan , officially the Republic of Azerbaijan is the largest country in the Caucasus region of Eurasia. Located at the crossroads of Western Asia and Eastern Europe, it is bounded by the Caspian Sea to the east, Russia to the north, Georgia to the northwest, Armenia to the west, and Iran to...
, to a wealthy Russian 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 Chukovsky
Korney Ivanovich Chukovsky was one of the most popular children's poets in the Russian language. His poems, Doctor Aybolit , The Giant Roach , The Crocodile , and Wash'em'clean have been favourites with many generations of Russophone children...
, who was thus Henrietta's half-brother). Vladimir Rokhlin's father Abram Veniaminovich Rokhin was a well-known social democrat (he was imprisoned during Stalin's Great Purge
Great Purge
The Great Purge was a series of campaigns of political repression and persecution in the Soviet Union orchestrated by Joseph Stalin from 1936 to 1938...
, and executed in 1941).
Vladimir Rokhlin entered Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
in 1935. His advisor was Abraham Plessner
Abraham Plessner
Abraham Plessner was a Russian mathematician. He was born on February 13, 1900 in Lodz, which is now in Poland. He studied at secondary school where he was taught in Russian, German, and Polish. He studied at the University of Giessen where he studied under Schlesinger and Friedrich Engel. He also...
. He volunteered for the army in 1941, leading to four years as a prisoner
Prisoner of war
A prisoner of war or enemy prisoner of war is a person, whether civilian or combatant, who is held in custody by an enemy power during or immediately after an armed conflict...
of a German war camp, and then two years in a Soviet camp
Gulag
The Gulag was the government agency that administered the main Soviet forced labor camp systems. While the camps housed a wide range of convicts, from petty criminals to political prisoners, large numbers were convicted by simplified procedures, such as NKVD troikas and other instruments of...
after the end of the war. He then returned to mathematics.
Since 1959 he was at Leningrad State University, where he was a very influential teacher.
His students include Yakov Eliashberg
Yakov Eliashberg
Yakov Eliashberg is a Russian mathematician. He received his Ph.D. from Leningrad University in 1972 under the direction of Vladimir Rokhlin. From 1972 to 1979 he taught at the Syktyvkar State University of Komi Republic of Russia and from 1980 to 1987 worked in industry as the head of a computer...
, Mikhail Gromov, Anatoly Vershik
Anatoly Vershik
Anatoly Moiseevich Vershik is a Soviet and Russian mathematician. He is most famous for his joint work with Sergey V. Kerov on representations of infinite symmetric groups and applications to the longest increasing subsequences....
and Oleg Viro
Oleg Viro
Oleg Viro is a 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 a result of 1952Rokhlin's theorem
In 4-dimensional topology, a branch of mathematics, Rokhlin's theorem states that if a smooth, compact 4-manifold M has a spin structure , then the signature of its intersection form, a quadratic form on the second cohomology group H2, is divisible by 16...
on the signature
Signature (topology)
In the mathematical field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension d=4k divisible by four ....
of 4-manifold
4-manifold
In mathematics, 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...
s, which was subsequently generalised by Hirzebruch. He also worked in the theory of characteristic classes, homotopy theory and cobordism theory.
In measure theory, Rokhlin introduced what is now called Rokhlin partitions. He introduced the notion of standard probability space
Standard probability space
In probability theory, a standard probability space is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940...
, and characterised such spaces up to isomorphism mod 0.
Family
His son Vladimir Rokhlin, Jr. is a well-known mathematician and computer scientist at Yale.Rokhlin's uncle was Korney Chukovsky
Korney Chukovsky
Korney Ivanovich Chukovsky was one of the most popular children's poets in the Russian language. His poems, Doctor Aybolit , The Giant Roach , The Crocodile , and Wash'em'clean have been favourites with many generations of Russophone children...
, a well known Russian
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
poet, most famous for his popular children's books.