New Action-Induced Nested Classes of Groups and Jump (Co)homology

Details New Action-Induced Nested Classes of Groups and Jump (Co)homology New Action-Induced Nested Classes of Groups and Jump (Co)homology

2009-11-03

arxiv.org/abs/0911.0541v1

Mathematics

Algebraic Topology

21 pages

Scientific paper

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 as well as new characterizations for some well-known classes, such as virtually polycyclic groups. We generalize properties of the virtual cohomological dimension of a group to groups with jump (co)homology and prove that a core subclass of a new class of groups has jump (co)homology.

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