On the rank of the double cohomology of moment-angle complexes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911838549049344 |
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| author | Zhang, Zhilei |
| author_facet | Zhang, Zhilei |
| contents | In [6], the authors construct a cochain complex $C\!H^*(\mathcal{Z}_{\mathcal{K}})$ on the cohomology of a moment-angle complex $\mathcal{Z}_{\mathcal{K}}$ and call the resulting cohomology the double cohomology, $H\!H^*(\mathcal{Z}_{\mathcal{K}})$. In this paper, we study the change of rank in double cohomology after gluing an $n$-simplex to a simplicial complex $\mathcal{K}$ in certain conditions. As an application, we give a positive answer to an open problem in [6]: For any even integer $r$, there always exists a simlicial complex $\mathcal{K}$ such that $\operatorname{rank} H\!H^*(\mathcal{Z}_{\mathcal{K}})=r$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the rank of the double cohomology of moment-angle complexes Zhang, Zhilei Algebraic Topology 13F55, 55N10, 55U10 In [6], the authors construct a cochain complex $C\!H^*(\mathcal{Z}_{\mathcal{K}})$ on the cohomology of a moment-angle complex $\mathcal{Z}_{\mathcal{K}}$ and call the resulting cohomology the double cohomology, $H\!H^*(\mathcal{Z}_{\mathcal{K}})$. In this paper, we study the change of rank in double cohomology after gluing an $n$-simplex to a simplicial complex $\mathcal{K}$ in certain conditions. As an application, we give a positive answer to an open problem in [6]: For any even integer $r$, there always exists a simlicial complex $\mathcal{K}$ such that $\operatorname{rank} H\!H^*(\mathcal{Z}_{\mathcal{K}})=r$. |
| title | On the rank of the double cohomology of moment-angle complexes |
| topic | Algebraic Topology 13F55, 55N10, 55U10 |
| url | https://arxiv.org/abs/2404.06763 |