Low-dimensional bounded cohomology and extensions of groups
Low-dimensional bounded cohomology and extensions of groups
复制标题
低维有界上同调和群的扩张
DOI：
10.7146/math.scand.a-114969
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发表时间：
2017
影响因子：
0.5
通讯作者：
Nicolaus Heuer
中科院分区：
文献类型：
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作者：
Nicolaus Heuer
群的有界上同调在1982年由Gromov在他的开创性论文M. Gromov， Volume and Bounded上同调，Inst. Hautes Études Sci。出版。数学。(1982),没有。56岁的5 - 99。从那时起，它引发了几何群论的大量研究。然而，即使对于最基本的“非正弯曲”群，显式计算有界上同调也是出了名的困难。另一方面，在$2$和$3$维度上的普通群上同，有一个众所周知的关于群扩展的解释。本文的目的是使这一解释适用于有界群上同调。这将涉及到K. Fujiwara和M. Kapovich在《论非交换目标的拟同态》中定义和研究的拟同态。功能。肛门26 (2016),no。2, 478 - 519。
Bounded cohomology of groups was first studied by Gromov in 1982 in his seminal paper M. Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. (1982), no. 56, 5–99. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic “non-positively curved” groups. On the other hand, there is a well-known interpretation of ordinary group cohomology in dimension $2$ and $3$ in terms of group extensions. The aim of this paper is to make this interpretation available for bounded group cohomology. This will involve quasihomomorphisms as defined and studied by K. Fujiwara and M. Kapovich, On quasihomomorphisms with noncommutative targets, Geom. Funct. Anal. 26 (2016), no. 2, 478–519.