algebraic topology oor Viëtnamees
algebraic topology
en
That branch of topology that associates objects from abstract algebra to topological spaces.
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en
branch of mathematics
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And it gradually grew to be a very important field in mathematics: algebraic topology, geometry.
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His work on topology was summed up in his monograph Algebraic Topology (1942).
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You have an understanding of differential calculus and at least one year of algebraic topology?
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In 2005 Novikov was awarded the Wolf Prize for his contributions to algebraic topology, differential topology and to mathematical physics.
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Henri Paul Cartan (French: ; 8 July 1904 – 13 August 2008) was a French mathematician with substantial contributions in algebraic topology.
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So that was the first sort of thrust, from the mid-1700s, into a subject which is now called algebraic topology.
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Similarly, the hairy ball theorem of algebraic topology says that "one cannot comb the hair flat on a hairy ball without creating a cowlick."
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Topology in all its many ramifications may have been the greatest growth area in 20th-century mathematics; it includes point-set topology, set-theoretic topology, algebraic topology and differential topology.
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In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.
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In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
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Its algebraic structure and topology make it into a Lie group, a type of topological group.
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Jean Alexandre Eugène Dieudonné (French: ; 1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology.
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In 1936, he published a long paper that included Stone's representation theorem for Boolean algebras, an important result in mathematical logic, topology, universal algebra and category theory.
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Group representations are an organizing principle in the theory of finite groups, Lie groups, algebraic groups and topological groups, especially (locally) compact groups.
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The Zariski topology is defined algebraically on the spectrum of a ring or an algebraic variety.
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In the application of topology to algebraic geometry, he followed the work of Charles Émile Picard, whom he had heard lecture in Paris at the École Centrale Paris.
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Noether's suggestion that topology be studied algebraically was adopted immediately by Hopf, Alexandrov, and others, and it became a frequent topic of discussion among the mathematicians of Göttingen.
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Finding algebraic equations, the solutions of which have the topology of a Möbius strip, is straightforward, but, in general, these equations do not describe the same geometric shape that one gets from the twisted paper model described above.
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Pham in the 1960s applied Thom's methods of differential topology to Landau singularities and in the 1970s worked with Bernard Teissier on singularities of systems of plane algebraic curves.
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According to the account of Alexandrov, Noether attended lectures given by Heinz Hopf and by him in the summers of 1926 and 1927, where "she continually made observations which were often deep and subtle" and he continues that, When ... she first became acquainted with a systematic construction of combinatorial topology, she immediately observed that it would be worthwhile to study directly the groups of algebraic complexes and cycles of a given polyhedron and the subgroup of the cycle group consisting of cycles homologous to zero; instead of the usual definition of Betti numbers, she suggested immediately defining the Betti group as the complementary (quotient) group of the group of all cycles by the subgroup of cycles homologous to zero.
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