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 ?
Objective: This research proposal is in mathematics, its content is part of algebraic topology and homotopy theory.
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.
We assume familiarity with the basic algebraic topology of simplicial complexes; see, e.
Working out the odds on the turn - no problem mate I've just got my head round algebraic topology.
The book can be used for an introduction to differential and algebraic topology, and for a quick presentation of homology and cohomology in a course on differential geometry.
Those faculty members who object to private donors building athletic facilities seem to have heard a theory somewhere that rich dudes who don't give their money to linebackers give it to the math department instead to improve knowledge of algebraic topology.
This project concerns an abstract and notoriously difficult-to-calculate notion of algebraic topology - Morse Homology, as developed by Morse, Conley, Witten, and Floer.
The textbook is for a two-semester first course in algebraic topology, but Shastri does not recommend trying to cover everything in just two semesters, because there is enough material that instructors have considerable leeway in selecting what they teach.
Rogness developed a fascination with algebraic topology, which became his area of study in graduate school.