mathematics

Vladimir Abramovich Rokhlin

Vladimir Abramovich Rokhlin is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Vladimir Abramovich Rokhlin rather than just read about it. In short: Vladimir Abramovich Rokhlin (Russian: Владимир Абрамович Рохлин; 23 August 1919 – 3 December 1984) was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry, measure theory, probability theory, ergodic theory and entropy theory. Life Vladimir Abramovich Rokhlin was born in Baku, Azerbaijan, to a wealthy Jewish family.

Key takeaways

Vladimir Abramovich Rokhlin belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Vladimir Abramovich Rokhlin to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Vladimir Abramovich Rokhlin from memory before moving on to harder problems.

Reference excerpt

Vladimir Abramovich Rokhlin (Russian: Владимир Абрамович Рохлин; 23 August 1919 – 3 December 1984) was a Soviet mathematician, who made numerous contributions in algebraic topology, geometry, measure theory, probability theory, ergodic theory and entropy theory.

Life Vladimir Abramovich Rokhlin was born in Baku, 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. 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 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, he was released in December 1946 and allowed to return to Moscow, after which he returned to mathematics. At Pontryagin's suggestion, he joined Steklov Institute of Mathematics as Pontryagin's official research assistant. In the 1950s, during the anti-cosmopolitan campaign, 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. 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, since 1957 he has been a professor of the Department of Mathematics at the Kolomna Pedagogical Institute. In 1959 Rokhlin joined Leningrad State University as a faculty member. He died in 1984 in Leningrad. His students include Viatcheslav Kharlamov, Yakov Eliashberg, Mikhail Gromov, Nikolai V. Ivanov, Anatoly Vershik and Oleg Viro.

Work Rokhlin's contributions to topology include Rokhlin's theorem, a result of 1952 on the signature of 4-manifolds. He also worked in the theory of characteristic classes, homotopy theory, cobordism theory, and in the topology of real algebraic varieties. In measure theory, Rokhlin introduced what are now called Rokhlin partitions. He introduced the notion of standard probability space, 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. Rokhlin's uncle was Korney Chukovsky, a well-known Russian poet, most famous for his popular children's books.

Illustrations

Vladimir Abramovich Rokhlin illustration

Worked examples

Example 1 — a first encounter with Vladimir Abramovich Rokhlin

Start with the simplest possible case. Write down what Vladimir Abramovich Rokhlin claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vladimir Abramovich Rokhlin before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vladimir Abramovich Rokhlin ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vladimir Abramovich Rokhlin

In research: Vladimir Abramovich Rokhlin appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Vladimir Abramovich Rokhlin in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Vladimir Abramovich Rokhlin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1919 births, 1984 deaths, 20th-century Russian Jews, so understanding it makes those chapters shorter.
In everyday life: Look for Vladimir Abramovich Rokhlin outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Vladimir Abramovich Rokhlin in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vladimir Abramovich Rokhlin means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Vladimir Abramovich Rokhlin out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vladimir Abramovich Rokhlin in simple terms?

Why does Vladimir Abramovich Rokhlin matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vladimir Abramovich Rokhlin?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vladimir Abramovich Rokhlin.