连接上同调与双同调

arXiv - MATH - Algebraic Topology Pub Date : 2024-06-26 DOI:arxiv-2406.18778

Luigi Caputi, Daniele Celoria, Carlo Collari

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摘要

我们利用梅耶-维托里斯谱序论证，建立了有限单纯复数的0度uberhomology和双重homology之间的同构关系。我们通过提供例子和一些结果澄清了这些理论之间的对应关系；特别是，我们证明了（uberhomology）群检测到了标准单纯形，而且双同调的对角线与连通支配多项式有关。

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Bridging between überhomology and double homology

We establish an isomorphism between the 0-degree \"uberhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify the correspondence between these theories by providing examples and some consequences; in particular, we show that \"uberhomology groups detect the standard simplex, and that the double homology's diagonal is related to the connected domination polynomial.

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arXiv - MATH - Algebraic Topology

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