Can I say that only maximal simplices in a simplicial complex determine the homology group? If not what's wrong?


put on hold as unclear what you're asking by David White, LSpice, user44191, Ivan Izmestiev, Sean Lawton 2 days ago

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    $\begingroup$ What exactly do you mean by "maximal simplices"? $\endgroup$ – Greg Friedman May 16 at 7:40
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    $\begingroup$ ... and what do you mean by the homology group, as there are infinitely many homology groups (which may be trivial). You need to expand the question to be more precise. $\endgroup$ – Tim Porter May 16 at 9:29
  • $\begingroup$ The set of maximal faces determines the whole simplicial complex, so in this sense it determines all of its properties. $\endgroup$ – Michal Adamaszek May 16 at 10:09