# Simplicial complexes with lattice structures

@article{Bergman2016SimplicialCW, title={Simplicial complexes with lattice structures}, author={George M. Bergman}, journal={arXiv: Rings and Algebras}, year={2016} }

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

Taxotopy Theory of Posets I: van Kampen Theorems

- Mathematics
- 2015

Given functors $F,G:\mathcal C\to\mathcal D$ between small categories, when is it possible to say that $F$ can be "continuously deformed" into $G$ in a manner that is not necessarily reversible? In…

Compatibility of book-spaces with certain identities

- Mathematics
- 2017

This paper is a brief study of the equations compatible with the (topological) n-book for all $${n \geq 2}$$n≥2. For each n, we exhibit an equation-set (an extension of lattice theory) that is…

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