Can I say that only maximal simplices in a simplicial complex determine the homology group? If not what's wrong?
0
put on hold as unclear what you're asking by David White, LSpice, user44191, Ivan Izmestiev, Sean Lawton 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

1$\begingroup$ What exactly do you mean by "maximal simplices"? $\endgroup$ – Greg Friedman May 16 at 7:40

1$\begingroup$ ... 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