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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.12923 |
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| _version_ | 1866929506642558976 |
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| author | Aten, Charlotte |
| author_facet | Aten, Charlotte |
| contents | In 2017, Walter Taylor showed that there exist $2$-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 $n$-dimensional simplicial complexes with the same property exist. We do this by giving, for each $n\ge2$, an infinite family of compact simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12923 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-dimensional book-spaces Aten, Charlotte Rings and Algebras Combinatorics 06B30, 57Q99 In 2017, Walter Taylor showed that there exist $2$-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 $n$-dimensional simplicial complexes with the same property exist. We do this by giving, for each $n\ge2$, an infinite family of compact simplicial complexes which admit the structure of topological modular lattice but not topological distributive lattice. |
| title | Higher-dimensional book-spaces |
| topic | Rings and Algebras Combinatorics 06B30, 57Q99 |
| url | https://arxiv.org/abs/2409.12923 |