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Meyer Bockstein
Meyer Bockstein (also Меер Феликсович Бокштейн or Meer Feliksovich Bokshtein or Bokstein) (4 October 1913 to 2 May 1990) was a topologist from Moscow who introduced the Bockstein homomorphism. The Bockstein spectral sequence In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod ''p'' coefficients and the homology reduced mod ''p''. It is named after Meyer Bockstein. Definition Let ''C'' be a chain complex o ... is named after him. References * * Russian Jewish Encyclopedia(Entry 791) {{DEFAULTSORT:Bockstein, Meyer F. Topologists 1913 births 1990 deaths Mathematicians from Moscow Soviet mathematicians ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topologist
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 residents within the city limits, over 17 million residents in the urban area, and over 21.5 million residents in the metropolitan area. The city covers an area of , while the urban area covers , and the metropolitan area covers over . Moscow is among the world's largest cities; being the most populous city entirely in Europe, the largest urban and metropolitan area in Europe, and the largest city by land area on the European continent. First documented in 1147, Moscow grew to become a prosperous and powerful city that served as the capital of the Grand Duchy that bears its name. When the Grand Duchy of Moscow evolved into the Tsardom of Russia, Moscow remained the political and economic center for most of the Tsardom's history. When ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bockstein Homomorphism
In homological algebra, the Bockstein homomorphism, introduced by , is a connecting homomorphism associated with a short exact sequence :0 \to P \to Q \to R \to 0 of abelian groups, when they are introduced as coefficients into a chain complex ''C'', and which appears in the homology groups as a homomorphism reducing degree by one, :\beta\colon H_i(C, R) \to H_(C,P). To be more precise, ''C'' should be a complex of free, or at least torsion-free, abelian groups, and the homology is of the complexes formed by tensor product with ''C'' (some flat module condition should enter). The construction of β is by the usual argument (snake lemma). A similar construction applies to cohomology groups, this time increasing degree by one. Thus we have :\beta\colon H^i(C, R) \to H^(C,P). The Bockstein homomorphism \beta associated to the coefficient sequence :0 \to \Z/p\Z\to \Z/p^2\Z\to \Z/p\Z\to 0 is used as one of the generators of the Steenrod algebra. This Bockstein homomorphism has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bockstein Spectral Sequence
In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod ''p'' coefficients and the homology reduced mod ''p''. It is named after Meyer Bockstein. Definition Let ''C'' be a chain complex of torsion-free abelian groups and ''p'' a prime number. Then we have the exact sequence: :0 \longrightarrow C \overset\longrightarrow C \overset \longrightarrow C \otimes \Z/p \longrightarrow 0. Taking integral homology ''H'', we get the exact couple of "doubly graded" abelian groups: :H_*(C) \overset \longrightarrow H_*(C) \overset \longrightarrow H_*(C \otimes \Z/p) \overset \longrightarrow. where the grading goes: H_*(C)_ = H_(C) and the same for H_*(C \otimes \Z/p),\deg i = (1, -1), \deg j = (0, 0), \deg k = (-1, 0). This gives the first page of the spectral sequence: we take E_^1 = H_(C \otimes \Z/p) with the differential ^1 d = j \circ k. The derived couple of the above exact couple then gives the second page and so forth. Expli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1913 Births
Events January * January 5 – First Balkan War: Battle of Lemnos (1913), Battle of Lemnos – Greek admiral Pavlos Kountouriotis forces the Turkish fleet to retreat to its base within the Dardanelles, from which it will not venture for the rest of the war. * January 13 – Edward Carson founds the (first) Ulster Volunteers, Ulster Volunteer Force, by unifying several existing Ulster loyalism, loyalist militias to resist home rule for Ireland. * January 23 – 1913 Ottoman coup d'état: Ismail Enver comes to power. * January – Stalin (whose first article using this name is published this month) travels to Vienna to carry out research. Until he leaves on February 16 the city is home simultaneously to him, Hitler, Trotsky and Josip Broz Tito, Tito alongside Alban Berg, Berg, Freud and Jung and Ludwig Wittgenstein, Ludwig and Paul Wittgenstein. February * February 1 – New York City's Grand Central Terminal, having been rebuilt, reopens as the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1990 Deaths
Year 199 ( CXCIX) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was sometimes known as year 952 ''Ab urbe condita''. The denomination 199 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Mesopotamia is partitioned into two Roman provinces divided by the Euphrates, Mesopotamia and Osroene. * Emperor Septimius Severus lays siege to the city-state Hatra in Central-Mesopotamia, but fails to capture the city despite breaching the walls. * Two new legions, I Parthica and III Parthica, are formed as a permanent garrison. China * Battle of Yijing: Chinese warlord Yuan Shao defeats Gongsun Zan. Korea * Geodeung succeeds Suro of Geumgwan Gaya, as king of the Korean kingdom of Gaya (traditional date). By topic Religion * Pope Zephyrinus succeeds Pope Vic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematicians From Moscow
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 One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
