Higher-dimensional book-spaces
Charlotte Aten

TL;DR
This paper constructs, for each dimension n ≥ 2, infinite families of compact simplicial complexes that are topological modular lattices but not topological distributive lattices, answering a question posed by Walter Taylor.
Contribution
It extends Taylor's 2017 result by providing explicit examples of higher-dimensional complexes with the same lattice properties.
Findings
Existence of infinite families of such complexes for all n ≥ 2
Construction of complexes that are modular but not distributive
Answer to Taylor's open question
Abstract
In 2017, Walter Taylor showed that there exist -dimensional simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattice. We give a positive answer to his question as to whether -dimensional simplicial complexes with the same property exist. We do this by giving, for each , an infinite family of compact simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattice.
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Taxonomy
TopicsComputational Geometry and Mesh Generation
