m-Contiguity Distance
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915938450800640 |
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| author | Yazici, Nilay Ekiz Kuanyshov, Nursultan Borat, Ayse |
| author_facet | Yazici, Nilay Ekiz Kuanyshov, Nursultan Borat, Ayse |
| contents | In this paper, we systematically develop the $m$-contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of invariants that approximate the contiguity distance from below. The fundamental properties of $m$-contiguity distance are established, including its behaviour under barycentric subdivision, under compositions, and a categorical product inequality. As applications of this theory, we define the $m$-simplicial Lusternik-Schnirelmann category and the $m$-discrete topological complexity, proving that each arises naturally as a special case of $m$-contiguity distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | m-Contiguity Distance Yazici, Nilay Ekiz Kuanyshov, Nursultan Borat, Ayse Algebraic Topology 55M30, 55U10, 55U05 In this paper, we systematically develop the $m$-contiguity distance between simplicial maps as a discrete approximation framework for homotopical complexity in the category of simplicial complexes. We construct an increasing sequence of invariants that approximate the contiguity distance from below. The fundamental properties of $m$-contiguity distance are established, including its behaviour under barycentric subdivision, under compositions, and a categorical product inequality. As applications of this theory, we define the $m$-simplicial Lusternik-Schnirelmann category and the $m$-discrete topological complexity, proving that each arises naturally as a special case of $m$-contiguity distance. |
| title | m-Contiguity Distance |
| topic | Algebraic Topology 55M30, 55U10, 55U05 |
| url | https://arxiv.org/abs/2602.14680 |