algebraic topology


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algebraic topology

[¦al·jə¦brā·ik tə′päl·ə·jē]
(mathematics)
The study of topological properties of figures using the methods of abstract algebra; includes homotopy theory, homology theory, and cohomology theory.
References in periodicals archive ?
Stavans, Application of algebraic topology to homologous recombination of DNA, iScience, 4, (2018), 64-67
Thomas presents her lecture notes for a graduate course for students with a background in basic group theory including group actions, a first course in algebraic topology, and some familiarity with Riemannian geometry, particularly the geometry of the hyperbolic plane.
This is a tool developed from algebraic topology, which summarizes the whole multiscale representation compactly in the form of a persistence diagram.
Hosted at one of the major centres for algebraic topology in the world and supervised by a world leader in homotopical group theory, The project will have a substantial impact on the er~s career by deepening and broadening his research expertise, Especially concerning p-compact groups and cohomology of finite groups; By significantly broadening his research network; And by solidifying his position as a trailblazer and leader in applying techniques from string topology to tackle difficult problems in group homology and cohomology."
[2] Hatcher, A.: Algebraic Topology, Cambridge University Press, Cambridge, 2002.
Jean-Pierre Serre's mathematical contributions, leading to a Fields Medal in 1954, were largely in the field of algebraic topology, but his later work ranged widely--within algebraic geometry, group theory, and especially number theory.
The Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety.
A few years later, Poincare stated the Poincare duality and provided a preliminary proof (2) in his 1895 seminal paper Analysis situs, which marked the formal establishment of algebraic topology (Ferreiros, 2010b).
User's Guide to Algebraic Topology. Dordrecht, Netherlands: Kluwer.
He assumes students are familiar with homological algebra, algebraic topology based on different forms, and de Rham cohomology.
Proved by the work of French mathematician Jean-Pierre Serre (who has made fundamental contributions to algebraic topology, algebraic geometry, and algebraic number theory) and American mathematician John Torrence Tate, Jr.
Within the discipline of mathematics, Gray argues that Poincare's chief contribution was the formulation of algebraic topology. Also significant were his studies of algebraic geometry, the theory of transformation groups, and number theory.