On the classifying space of the family of virtually cyclic subgroups

Abstract

We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually cyclic. We give examples of groups for which the difference of the minimal dimensions of the classifying spaces of virtually cyclic and of finite subgroups is -1, 0 and 1, and show in many cases that no other values can occur.

arXiv commentFinal version, to appear in the Proceedings in honour of Farrel and Jones in Pure and Applied Mathematic Quarterly. 45 pages

References in corpus (3)

• On the domain of the assembly map in algebraic K-theory
• K- and L-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by Z/4
• Classifying spaces for proper actions of locally-finite groups

Cited by in corpus (9)

• Cohomological Finiteness Conditions in Bredon Cohomology
• Lower algebraic K-theory of certain reflection groups
• On the classifying space of the family of finite and of virtually cyclic subgroups for CAT(0)-groups
• Topological K-(co-)homology of classifying spaces of discrete groups
• Classifying spaces for knots: New bridges between knot theory and algebraic number theory
• On the K- and L-theory of hyperbolic and virtually finitely generated abelian groups
• On the group cohomology of the semi-direct product Z^n rtimes Z/m and a conjecture of Adem-Ge-Pan-Petrosyan
• The Virtually Cyclic Classifying Space of the Heisenberg Group
• Complete Bredon cohomology and its applications to hierarchically defined groups