Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914906171768832 |
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| author | Oganisian, Victoria Panov, Taras |
| author_facet | Oganisian, Victoria Panov, Taras |
| contents | We prove that the moment-angle complex $\mathcal Z_K$ corresponding to a 3-dimensional simplicial sphere $K$ has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) $K$ is the boundary of a 4-dimensional cross-polytope, or (b) the one-skeleton of $K$ is a chordal graph, or (c) there are only two missing edges in $K$ and they form a chordless 4-cycle. For simplicial spheres $K$ of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism $H^*(\mathcal Z_K)\cong H^*(M)$ where $M$ is a connected sum of products of spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres Oganisian, Victoria Panov, Taras Algebraic Topology Combinatorics 57S12, 57N65 We prove that the moment-angle complex $\mathcal Z_K$ corresponding to a 3-dimensional simplicial sphere $K$ has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) $K$ is the boundary of a 4-dimensional cross-polytope, or (b) the one-skeleton of $K$ is a chordal graph, or (c) there are only two missing edges in $K$ and they form a chordless 4-cycle. For simplicial spheres $K$ of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism $H^*(\mathcal Z_K)\cong H^*(M)$ where $M$ is a connected sum of products of spheres. |
| title | Moment-angle manifolds corresponding to three-dimensional simplicial spheres, chordality and connected sums of products of spheres |
| topic | Algebraic Topology Combinatorics 57S12, 57N65 |
| url | https://arxiv.org/abs/2408.04843 |