algebraic topology
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English
Noun
algebraic topology (uncountable)
- (mathematics) The branch of mathematics that uses tools from abstract algebra to study topological spaces.
- The basic goal of algebraic topology is to find algebraic invariants that classify topological spaces up to homeomorphism, although most usually classify up to homotopy (homeomorphism being a special case of homotopy).
- Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible.
- 1969, Emil Artin, Hel Braun, Introduction to Algebraic Topology, C. E. Merrill Publishing Company,
- Professor Emil Artin lectured on algebraic topology during the winter semester of 1959–60.
- 2001, James F. Davis, Paul Kirk, Lecture Notes in Algebraic Topology, American Mathematical Society, page xii:
- The material in Chapters 7 (Obstruction Theory and Eilenberg-MacLane Spaces) and 8 (Bordism, Spectra, and Generalized Homology) introduces the student to the modern perspective in algebraic topology.
- 2002, Allen Hatcher, Algebraic Topology, Cambridge University Press:
Synonyms
- (branch of mathematics): combinatorial topology (obsolete)
Translations
branch of mathematics
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