High Quality Content by WIKIPEDIA articles! In mathematics, a simplicial manifold is a "simplicial complex" fulfilling certain conditions involving the local structure of the complex, usually concerning some or all "links" or "stars", which then are assumed to be sphere- resp. ball-like in some sense - typically homotopically, homologically or combinatorially, but there are also other ways to formulate simplicial manifold criteria. Simplicial complexes are mainly either "geometrical" or "abstract". The former is usually (non-exhaustively) encountered as "simplicial" structures, the local structure of which strongly relates to some well-behaved subspace of some Euclidian space in a way that allow a well-defined concept of "dimension". The abstract simplicial maniolds is most likely to appear within algebraic topology or combinatorics. Through "realization functors", "abstract" and "geometrical" simplicial complexes are related in some clarifying way.

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