Moment angle complexes and duality for tight manifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911603666976768 |
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| author | Kishimoto, Daisuke Stanley, Donald Ruiz, Carlos Gabriel Valenzuela |
| author_facet | Kishimoto, Daisuke Stanley, Donald Ruiz, Carlos Gabriel Valenzuela |
| contents | For a field $\mathbb{F}$ and a triangulated compact $\mathbb{F}$-orientable manifold, consider the homology of the associated Moment-Angle ccomplex $H_*(\mathcal{Z}_{\mathcal{K}})$. We show the total homology rank $β(\mathcal{Z}_{\mathcal{K}})$ satisfies the inequality $β(\mathcal{Z}_{\mathcal{K}};\mathbb{F})\geq 2^{m-1}(β(\mathcal{K};\mathbb{F})-2)+2$, with equality occurring exactly when the triangulation is $\mathbb{F}$-tight. Using Lefschetz duality, we introduce a short exact sequence of functors that, in turn, introduces a new duality theorem in Double Homology for tight manifold triangulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16739 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Moment angle complexes and duality for tight manifolds Kishimoto, Daisuke Stanley, Donald Ruiz, Carlos Gabriel Valenzuela Algebraic Topology 13F55, 57Q15, 55835 For a field $\mathbb{F}$ and a triangulated compact $\mathbb{F}$-orientable manifold, consider the homology of the associated Moment-Angle ccomplex $H_*(\mathcal{Z}_{\mathcal{K}})$. We show the total homology rank $β(\mathcal{Z}_{\mathcal{K}})$ satisfies the inequality $β(\mathcal{Z}_{\mathcal{K}};\mathbb{F})\geq 2^{m-1}(β(\mathcal{K};\mathbb{F})-2)+2$, with equality occurring exactly when the triangulation is $\mathbb{F}$-tight. Using Lefschetz duality, we introduce a short exact sequence of functors that, in turn, introduces a new duality theorem in Double Homology for tight manifold triangulations. |
| title | Moment angle complexes and duality for tight manifolds |
| topic | Algebraic Topology 13F55, 57Q15, 55835 |
| url | https://arxiv.org/abs/2604.16739 |