The Hauptvermutung, or "Main Conjecture," is a concept in topology, particularly in the field of algebraic topology. It refers to a conjecture about the nature of simplicial complexes and their triangulations. Specifically, the Hauptvermutung posits that if two simplicial complexes are homeomorphic (i.e., there is a continuous deformation between them without tearing or gluing), then they have the same number of simplices in each dimension.
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