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Geometric dimension of groups for the family of virtually cyclic subgroups

Authors
  • Degrijse, Dieter
  • Petrosyan, Nansen
Type
Preprint
Publication Date
Jun 05, 2012
Submission Date
Apr 16, 2012
Identifiers
arXiv ID: 1204.3482
Source
arXiv
License
Yellow
External links

Abstract

By studying commensurators of virtually cyclic groups, we prove that every elementary amenable group of finite Hirsch length h and cardinality aleph-n admits a finite dimensional classifying space with virtually cyclic stabilizers of dimension n+h+2. We also provide a criterion for groups that fit into an extension with torsion-free quotient to admit a finite dimensional classifying space with virtually cyclic stabilizers. Finally, we exhibit examples of integral linear groups of type F whose geometric dimension for the family of virtually cyclic subgroups is finite but arbitrarily larger than the geometric dimension for proper actions. This answers a question posed by W. Lueck.

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