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.
Applications of algebraic topology Classic applications of algebraic topology include: * The Brouwer fixed point theorem : every continuous map from the unit n-disk to itself has a fixed point. Source: Internet
A modern, geometrically flavoured introduction to algebraic topology. Source: Internet
Computer science Topological data analysis uses techniques from algebraic topology to determine the large scale structure of a set (for instance, determining if a cloud of points is spherical or toroidal ). Source: Internet
From about the 1920s onwards, it was realised that tensors play a basic role in algebraic topology (for example in the Künneth theorem ). Source: Internet
This convention is more common in applications to algebraic topology (such as simplicial homology ) than to the study of polytopes. Source: Internet
Researchers are exploring connections between dependent types (especially the identity type) and algebraic topology (specifically homotopy ). Source: Internet