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arXiv · 2608.11170

Eigenvalue growth of the discrete Hodge Laplacian across dimensions

Philipp Bartmann·Matthias Keller
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Abstract

We prove several bounds on the largest and smallest eigenvalues of the combinatorial Hodge Laplacian $Δ^H_k$ of a finite simplicial complex $Σ.$ As a consequence, we obtain new vanishing criteria for cohomology groups $H^k(Σ,\mathbb{R)}$ and confirm a conjecture of O on the dimensional monotonicity of the largest eigenvalue.

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Philipp Bartmann, Matthias Keller. 2026-08-21. Eigenvalue growth of the discrete Hodge Laplacian across dimensions. https://arxiv.org/abs/2608.11170

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