$${{\,\mathrm{{CAT}}\,}}(0)$$立方复合物上的中值准变形及其杯积

Pub Date : 2023-12-23 DOI:10.1007/s10711-023-00870-3

Benjamin Brück, Francesco Fournier-Facio, Clara Löh

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引用次数: 0

摘要

杯积是访问高界同调群的一种自然方法。我们将自由群的布鲁克斯类变的杯积的消失结果扩展到中位类变的杯积，即群作用于 ${{\,\mathrm{{CAT}\,}}(0)$ 立方复数的布鲁克斯类变。特别是，我们得到了作用于树的群和直角阿尔丁群的这种消失结果。此外，我们还概述了有界同调中杯积的消失结果的潜在应用。

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Median quasimorphisms on $${{\,\mathrm{{CAT}}\,}}(0)$$ cube complexes and their cup products

Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on ${{\,\mathrm{{CAT}}\,}}(0)$ cube complexes. In particular, we obtain such vanishing results for groups acting on trees and for right-angled Artin groups. Moreover, we outline potential applications of vanishing results for cup products in bounded cohomology.

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