The Hauptvermutung[a] of geometric topology is a now refuted conjecture asking whether any two triangulations of a triangulable space have subdivisions that are combinatorially equivalent, i.e. the subdivided triangulations are built up in the same combinatorial pattern. It was originally formulated as a conjecture in 1908 by Ernst Steinitz[1] and Heinrich Franz Friedrich Tietze,[2] but it is now known to be false.
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