Spherical complexes
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929680289890304 |
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| author | Faridi, Sara Holleben, Thiago |
| author_facet | Faridi, Sara Holleben, Thiago |
| contents | In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such complexes are independence complexes of ternary graphs and independence complexes of simplicial forests. We give criteria for when a spherical complex is acyclic, and describe the dimension of the sphere when it is not. We then apply our results to compute the Leray number of these complexes, and define combinatorial invariants for them which are counterparts to algebraic invariants of their Stanley-Reisner rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spherical complexes Faridi, Sara Holleben, Thiago Commutative Algebra Algebraic Topology Combinatorics 13F55, 05E40, 05E45, 55U10, 55P15 In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homology, or has the homology of a sphere. Examples of such complexes are independence complexes of ternary graphs and independence complexes of simplicial forests. We give criteria for when a spherical complex is acyclic, and describe the dimension of the sphere when it is not. We then apply our results to compute the Leray number of these complexes, and define combinatorial invariants for them which are counterparts to algebraic invariants of their Stanley-Reisner rings. |
| title | Spherical complexes |
| topic | Commutative Algebra Algebraic Topology Combinatorics 13F55, 05E40, 05E45, 55U10, 55P15 |
| url | https://arxiv.org/abs/2311.07727 |