论文标题
双曲线和有界价值的共同体学
Hyperbolicity and bounded-valued cohomology
论文作者
论文摘要
我们将Gersten定理概括为限制映射的溢流性，以$ \ ell^{\ infty} $ - 组的共同体学。这导致了对双曲线组的亚组的应用，有限生成的组的准等级区别以及$ \ ell^{\ iffty} $ - 共同体学计算一些众所周知的组。一路上，我们获得了$ fp_2（\ Mathbb Q）类型组的双曲线标准，以及那些满足理性同源线性等值不平等的人，回答了Arora和Martínez-Pedroza的问题。
We generalise a theorem of Gersten on surjectivity of the restriction map in $\ell^{\infty}$-cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and $\ell^{\infty}$-cohomology calculations for some well-known classes of groups. Along the way, we obtain hyperbolicity criteria for groups of type $FP_2(\mathbb Q)$ and for those satisfying a rational homological linear isoperimetric inequality, answering a question of Arora and Martínez-Pedroza.
