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

IF 0.5 4区数学 Q3 MATHEMATICS Geometriae Dedicata 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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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.

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