Mapping class group of a surface
= Mapping class group of a surface
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The mapping class group of a surface is a fundamental concept in the field of algebraic topology and differential geometry. Given a surface \\( S \\), the mapping class group, denoted \\( \\mathrm\{Mod\}(S) \\), consists of equivalence classes of orientation-preserving homeomorphisms of the surface modulo the action of homotopy.