Vertex-Minimal Triangulation of Complexes with Homology
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911293037871104 |
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| author | Kogan, Jon V. |
| author_facet | Kogan, Jon V. |
| contents | For a given pair of numbers $(d,k)$, we establish the minimal number of vertices in pure $d$-dimensional simplicial complexes with non-trivial homology in dimension $k$. Furthermore, we solve the problem under the additional constraint of strong connectivity with respect to any intermediate dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12164 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vertex-Minimal Triangulation of Complexes with Homology Kogan, Jon V. Combinatorics Algebraic Topology 55U10 (Primary) 05E45, 52C45 (Secondary) For a given pair of numbers $(d,k)$, we establish the minimal number of vertices in pure $d$-dimensional simplicial complexes with non-trivial homology in dimension $k$. Furthermore, we solve the problem under the additional constraint of strong connectivity with respect to any intermediate dimension. |
| title | Vertex-Minimal Triangulation of Complexes with Homology |
| topic | Combinatorics Algebraic Topology 55U10 (Primary) 05E45, 52C45 (Secondary) |
| url | https://arxiv.org/abs/2501.12164 |