تقرير
Right-angled Artin groups and the cohomology basis graph
| العنوان: | Right-angled Artin groups and the cohomology basis graph |
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| المؤلفون: | Flores, Ramón, Kahrobaei, Delaram, Koberda, Thomas, Coz, Corentin Le |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Combinatorics, Mathematics - Geometric Topology |
| الوصف: | Let $\Gamma$ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. From an arbitrary basis $\mathcal B$ of $H^1(A(\Gamma),\mathbb F)$ over an arbitrary field, we construct a natural graph $\Gamma_{\mathcal B}$ from the cup product, called the \emph{cohomology basis graph}. We show that $\Gamma_{\mathcal B}$ always contains $\Gamma$ as a subgraph. This provides an effective way to reconstruct the defining graph $\Gamma$ from the cohomology of $A(\Gamma)$, to characterize the planarity of the defining graph from the algebra of $A(\Gamma)$, and to recover many other natural graph-theoretic invariants. We also investigate the behavior of the cohomology basis graph under passage to elementary subminors, and show that it is not well-behaved under edge contraction. Comment: 18 pages, to appear in Proc. Edinburgh Math. Soc |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.05495 |
| رقم الأكسشن: | edsarx.2309.05495 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |