Homotopy type of shellable $q$-complexes and their homology groups
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910364184084480 |
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| author | Ghorpade, Sudhir R. Pratihar, Rakhi Randrianarisoa, Tovohery H. Verdure, Hugues Wilson, Glen |
| author_facet | Ghorpade, Sudhir R. Pratihar, Rakhi Randrianarisoa, Tovohery H. Verdure, Hugues Wilson, Glen |
| contents | The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to $q$-matroid complexes and determines singular homology groups for a subclass of these $q$-simplicial complexes. In this paper, we determine the homotopy type of shellable $q$-simplicial complexes. Moreover, we establish the shellability of order complexes from lexicographically shellable $q$-simplicial complexes, that include the $q$-matroid complexes. This results in a comprehensive determination of the homology groups for any lexicographically shellable $q$-complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy type of shellable $q$-complexes and their homology groups Ghorpade, Sudhir R. Pratihar, Rakhi Randrianarisoa, Tovohery H. Verdure, Hugues Wilson, Glen Combinatorics 05B35, 05A30, 52B22, 55N99 The theory of shellable simplicial complexes brings together combinatorics, algebra, and topology in a remarkable way. Initially introduced by Alder for $q$-simplicial complexes, recent work of Ghorpade, Pratihar, and Randrianarisoa extends the study of shellability to $q$-matroid complexes and determines singular homology groups for a subclass of these $q$-simplicial complexes. In this paper, we determine the homotopy type of shellable $q$-simplicial complexes. Moreover, we establish the shellability of order complexes from lexicographically shellable $q$-simplicial complexes, that include the $q$-matroid complexes. This results in a comprehensive determination of the homology groups for any lexicographically shellable $q$-complexes. |
| title | Homotopy type of shellable $q$-complexes and their homology groups |
| topic | Combinatorics 05B35, 05A30, 52B22, 55N99 |
| url | https://arxiv.org/abs/2403.07102 |