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Carlos Gabriel Valenzuela Ruiz

Publications and source records attributed to Carlos Gabriel Valenzuela Ruiz.

4 recordsLinked to original sources
arXiv2026

Moment angle complexes and duality for tight manifolds

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.

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arXiv2025

Double, über and poset homology

We present a comparison map between the uberhomology of a simplicial complex $\mathcal{K}$ and the double homology of its associated moment-angle complex $\mathcal{Z}_{\mathcal{K}}$. We show these two homology theories differ at three bidegrees, which depend on whether the complex $K$ is neighbourly or not.

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arXiv2024

Sphere Triangulations and their Double Homology

We study the double homology associated to triangulated spheres and present two results. First, we explicitly compute the double homology for minimum degree sphere triangulations. Using a spectral sequence argument, we compute the effect of removing a maximal simplex of a non-neighborly sphere triangulation. Using these results and computational aid we generate complexes with exotic double homology rank. We also relate the double homology of a complex with how neighborly it is.

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