AI 中文总结
该研究针对有限单纯复形的组合霍奇拉普拉斯算子特征值给出界的证明，得到上同调群新消失判据并证实相关单调性猜想。
AI 中文摘要
我们对有限单纯复形Σ的组合霍奇拉普拉斯算子Δ^H_k的最大与最小特征值证明了若干界，由此得到上同调群H^k(Σ,ℝ)的新消失判据，并证实了O提出的最大特征值维度单调性猜想。
英文摘要
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.
Commentsgeneralized Corollary 4.5 and Corollary 6.2, added Lemma 4.6 to relate our results to those of Lew, corrected some typos
