algebraic topology

Definitions

1. 1

   The branch of mathematics that uses tools from abstract algebra to study topological…

   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.

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