Back طوبولوجيا جبرية Arabic Topoloxía alxebraica AST Алгебраик топология Bashkir Алгебрична топология Bulgarian বীজগাণিতিক টপোলজি Bengali/Bangla Topologia algebraica Catalan Algebraická topologie Czech Algebraische Topologie German Αλγεβρική τοπολογία Greek Algebra topologio Esperanto
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence.
Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group.