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== Computational problems ==
{{Main|Simplicial complex recognition problem}}
The [[simplicial complex recognition problem]] is: given a finite ASC, decide whether its geometric realization is homeomorphic to a given geometric object. This problem is [[Undecidable problem|undecidable]] for any ''d''-dimensional manifolds for ''d'' ≥ 5{{Citation needed}}.
== Relation to other concepts ==
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