非圆柱形双曲群的有界上同调的零范数子空间

IF 1.1 3区 数学 Q1 MATHEMATICS
Federico Franceschini, R. Frigerio, M. B. Pozzetti, A. Sisto
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引用次数: 8

摘要

构造了绕圆的双曲三流形的组合体积形式。这些形式定义了有界上同调中的非平凡类。在引入了精确有界上同调上的一个新的半模后,利用这些组合类证明了在3次下,非圆柱形双曲群的有界上同调的零范数子空间是无限维的。在附录中,我们用同样的方法给出了一个下界的上同调证明,这个下界最初是由Brock给出的,是关于闭曲面的合拟anosov同胚映射环面体积上关于其Teichm\ uller平移距离的上同调证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The zero norm subspace of bounded cohomology of acylindrically hyperbolic groups
We construct combinatorial volume forms of hyperbolic three manifolds fibering over the circle. These forms define non-trivial classes in bounded cohomology. After introducing a new seminorm on exact bounded cohomology, we use these combinatorial classes to show that, in degree 3, the zero norm subspace of the bounded cohomology of an acylindrically hyperbolic group is infinite dimensional. In the appendix we use the same techniques to give a cohomological proof of a lower bound, originally due to Brock, on the volume of the mapping torus of a cobounded pseudo-Anosov homeomorphism of a closed surface in terms of its Teichm\"uller translation distance.
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来源期刊
CiteScore
1.60
自引率
0.00%
发文量
20
审稿时长
>12 weeks
期刊介绍: Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.
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