Full subcomplexes of Bier spheres
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911307380293632 |
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| author | Choi, Suyoung Yoon, Younghan Yu, Seonghyeon |
| author_facet | Choi, Suyoung Yoon, Younghan Yu, Seonghyeon |
| contents | Full subcomplexes of a simplicial complex encode essential structure for understanding the complex itself. For a simplicial complex $K$, possibly with a ghost vertex, the Bier sphere of $K$ is a simplicial sphere obtained as the deleted join of $K$ and its combinatorial Alexander dual. In this paper, we determine the homotopy types of all full subcomplexes of Bier spheres. As applications, we provide a formula for the bigraded Betti numbers of the Bier sphere of $K$ in terms of full subcomplexes of $K$, and we explicitly describe the cohomology of real toric manifolds associated with Bier spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05385 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Full subcomplexes of Bier spheres Choi, Suyoung Yoon, Younghan Yu, Seonghyeon Combinatorics Algebraic Topology 55U10, 57S12, 52B05, 13F55 Full subcomplexes of a simplicial complex encode essential structure for understanding the complex itself. For a simplicial complex $K$, possibly with a ghost vertex, the Bier sphere of $K$ is a simplicial sphere obtained as the deleted join of $K$ and its combinatorial Alexander dual. In this paper, we determine the homotopy types of all full subcomplexes of Bier spheres. As applications, we provide a formula for the bigraded Betti numbers of the Bier sphere of $K$ in terms of full subcomplexes of $K$, and we explicitly describe the cohomology of real toric manifolds associated with Bier spheres. |
| title | Full subcomplexes of Bier spheres |
| topic | Combinatorics Algebraic Topology 55U10, 57S12, 52B05, 13F55 |
| url | https://arxiv.org/abs/2503.05385 |