Action-induced nested classes of groups and jump (co) homology

作者：Petrosyan Nansen^*

来源：Forum Mathematicum, 2015, 27(3): 1591-1612.

DOI：10.1515/forum-2012-0021

• Cellular action
• jump cohomology
• Hirsch length

Using fixed-point-free group actions, we set up a scheme to define nested classes of groups indexed over ordinals. Restricting to cellular actions on CW-complexes, we find new classes of groups as well as new characterizations for some well-known classes. We extend some of the properties of the cohomological dimension of a group to groups with jump (co) homology and study their implications to cellular actions on finite dimensional CW-complexes that satisfy a quite general homological condition.

• 出版日期2015-5