论文标题
中央扩展和有界的共同体学
Central extensions and bounded cohomology
论文作者
论文摘要
Gersten表明，有限生成的组的中心扩展是准时琐的，前提是其欧拉类是有界的。我们说，如果任何Quasi-Isimetrimenticaltimetripartiality在$ g $的欧拉类的欧拉类是有限的。我们展示有限生成的$ g $，该集团不满足财产QITB。这回答了Neumann和Reeves的问题，并为Wienhard和Blank提供了部分答案。我们还证明，属性QITB适用于大量组，包括符合的组，右角Artin组，具有正交外围亚组的相对双曲线组和3个manifold组。 最后，我们表明，如果格罗莫夫（Gromov）对差异形式的有限原始人的猜想，则属性QITB适用于每个有限呈现的组。
It was shown by Gersten that a central extension of a finitely generated group is quasi-isometrically trivial provided that its Euler class is bounded. We say that a finitely generated group $G$ satisfies Property QITB (quasi-isometrically trivial implies bounded) if the Euler class of any quasi-isometrically trivial central extension of $G$ is bounded. We exhibit a finitely generated group $G$ which does not satisfy Property QITB. This answers a question by Neumann and Reeves, and provides partial answers to related questions by Wienhard and Blank. We also prove that Property QITB holds for a large class of groups, including amenable groups, right-angled Artin groups, relatively hyperbolic groups with amenable peripheral subgroups, and 3-manifold groups. Finally, we show that Property QITB holds for every finitely presented group if a conjecture by Gromov on bounded primitives of differential forms holds as well.
