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** [[Nielsen–Thurston classification]] which characterizes homeomorphisms of a compact surface
* Thurston's eight model geometries, and the [[geometrization conjecture]]
* [[Symmetric space#Classification of Riemannian symmetric spaces|Classification of Riemannian symmetric spaces]]
==Algebra==
* [[Classification of finite simple groups]]
* [[Artin–Wedderburn theorem]] — a classification theorem for semisimple rings
* [[Classification of Clifford algebras]]
* [[Classification of low-dimensional real Lie algebras]]
* [[ADE classification]]
==Linear algebra==
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