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Thurston's Classification TheoremThurston's classification theorem is a result in mathematics that helps characterize the set of all maps of a surface back to itself. William Thurston's theorem completes the work initiated by Nielsen in the 1930s. The theorem states that every homeomorphism f:S → S is isotopic, relative to a finite set of punctures, to another homeomorphism that is either periodic or pseudo-Anosov, or reducible to a collection of them.
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