Simplicial complexes with lattice structures

  title={Simplicial complexes with lattice structures},
  author={George M. Bergman},
  journal={arXiv: Rings and Algebras},
  • 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… 
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