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arXiv · 2604.16739

Moment angle complexes and duality for tight manifolds

Daisuke Kishimoto·Donald Stanley·Carlos Gabriel Valenzuela Ruiz
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Abstract

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 $\beta(\mathcal{Z}_{\mathcal{K}})$ satisfies the inequality $\beta(\mathcal{Z}_{\mathcal{K}};\mathbb{F})\geq 2^{m-1}(\beta(\mathcal{K};\mathbb{F})-2)+2$, 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.

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Daisuke Kishimoto, Donald Stanley, Carlos Gabriel Valenzuela Ruiz. 2026-04-17. Moment angle complexes and duality for tight manifolds. https://arxiv.org/abs/2604.16739

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