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Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
-
Giovanni Gandini
and
Brita E. A. Nucinkis
Published/Copyright:
July 25, 2012
Abstract
Kropholler and Mislin conjectured that groups acting admissibly on a finite-dimensional G-CW-complex with finite stabilisers admit a finite-dimensional model for E𝔉G, the classifying space for proper actions. This conjecture is known to hold for groups with bounded torsion. In this note we consider a large class of groups 𝔘 containing the above and many known examples with unbounded torsion. We show that the conjecture holds for a large subclass of 𝔘.
Funding source: Leibniz-award of Wolfgang Lück
Funding source: EPSRC
Award Identifier / Grant number: EP/J016993/1
The authors thank the referee for helpful comments and suggestions, and for pointing out an improvement to our bound in the lemma in Remark 3.6.
Received: 2012-2-22
Revised: 2012-6-8
Published Online: 2012-7-25
Published in Print: 2015-1-1
© 2015 by De Gruyter
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Articles in the same Issue
- Frontmatter
- On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E
- Achievable sets in ℤn
- A criterion on oscillation and variation for the commutators of singular integral operators
- Some 𝐇1𝔉-groups with unbounded torsion and a conjecture of Kropholler and Mislin
- Goodwillie calculus and Whitehead products
- Computing Borel's regulator
- Applications of a transcendence criterion for reciprocal sums of binary linear recurrences
- BSDE and generalized Dirichlet forms: The infinite dimensional case
- Faithful representations of infinite-dimensional nilpotent Lie algebras
- Locally finitely presented categories with no flat objects
- A common generalization of metric, ultrametric and topological fixed point theorems
- Correction to A common generalization of metric, ultrametric and topological fixed point theorems [Forum Math. 27 (2015), 303–327]
- Erdős–Rényi graph, Szemerédi–Trotter type theorem, and sum-product estimates over finite rings
- Minimal support results for Schrödinger equations
- Dynamics for the focusing, energy-critical nonlinear Hartree equation
- A fixed point theorem for Lie groups acting on buildings and applications to Kac–Moody theory
- On effective determination of Maass forms from central values of Rankin–Selberg L-function
- On embedding left-ordered groups into division rings
- Conservation property of symmetric jump-diffusion processes
- Irreducible representations of Leavitt path algebras
- Commutators of elements of coprime orders in finite groups
- Endoscopy and the transfer from GSp(4) to GL(4)
- Cycles in Leavitt path algebras by means of idempotents
- On volumes determined by subsets of Euclidean space
