# Simplicial complexes with lattice structures

@article{Bergman2016SimplicialCW,
title={Simplicial complexes with lattice structures},
author={George M. Bergman},
journal={arXiv: Rings and Algebras},
year={2016}
}
• G. Bergman
• Published 29 January 2016
• Mathematics
• arXiv: Rings and Algebras
If $L$ is a finite lattice, we show that there is a natural topological lattice structure on the geometric realization of its order complex $\Delta(L)$ (definition recalled). Lattice-theoretically, the resulting object is a subdirect product of copies of $L$. We note properties of this construction and of some variants thereof, and pose several questions. For $M_3$ the $5$-element nondistributive modular lattice, $\Delta(M_3)$ is modular, but its underlying topological space does not admit a…
2 Citations
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