Simplicial Complexes with Lattice Structures
نویسنده
چکیده
If L is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex ∆(L) (definition recalled below). Lattice-theoretically, the resulting object is a subdirect product of copies of L. We note properties of this construction and of some variants, and pose several questions. For M3 the 5-element nondistributive modular lattice, ∆(M3) is modular, but its underlying topological space does not admit a structure of distributive lattice, answering a question of
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