有不诚实毛发的森林图和毛发图复合物上的差分

arXiv - MATH - Quantum Algebra Pub Date : 2024-07-07 DOI:arxiv-2407.05326

Nicolas Grunder

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引用次数: 0

摘要

我们研究具有有序和无序发丝的森林图复合体的同调，这些复合体的同调计算了一个组$\Gamma_{g,r}$族的同调，这个组概括了自由组的（外）自变群。我们给出了在这些复数上构造附加微分的例子和方法。这些微分可用于构造以标准复数的同调为起点的谱序列。我们将重点讨论这样一个序列，它将具有不同毛数的图的同调类联系起来，并计算其极限。

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Differentials on Forested and Hairy Graph Complexes with Dishonest Hairs

We study the cohomology of forested graph complexes with ordered and unordered hairs whose cohomology computes the cohomology of a family of groups $\Gamma_{g,r}$ that generalize the (outer) automorphism group of free groups. We give examples and a recipe for constructing additional differentials on these complexes. These differentials can be used to construct spectral sequences that start with the cohomology of the standard complexes. We focus on one such sequence that relates cohomology classes of graphs with different numbers of hairs and compute its limit.

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arXiv - MATH - Quantum Algebra

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