Cohomological finiteness conditions for elementary amenable groups

DOI10.1515/CRELLE.2009.090zbMath1202.20055MaRDI QIDQ3404370

Conchita Martínez-Pérez, Brita E. A. Nucinkis, Peter H. Kropholler

Publication date: 9 February 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

zbMATH Keywords

polycyclic-by-finite groupsclassifying spacesprojective resolutionscohomological dimensionconstructible groupscohomological finiteness conditionsHirsch numberselementary amenable groupsBredon finiteness conditions

Mathematics Subject Classification ID

Generalizations of solvable and nilpotent groups (20F19) Homological methods in group theory (20J05)

Related Items (19)

Bredon cohomological finiteness conditions for generalisations of Thompson groups. ⋮ Dimension invariants for groups admitting a cocompact model for proper actions ⋮ Abels's groups revisited. ⋮ Brown's criterion and classifying spaces for families ⋮ Graph-wreath products and finiteness conditions ⋮ Sigma theory for Bredon modules. ⋮ Cohomological finiteness conditions for Mackey and cohomological Mackey functors. ⋮ Groups of piecewise isometric permutations of lattice points, or Finitary rearrangements of tessellations ⋮ Homological dimension of elementary amenable groups ⋮ Coherence for elementary amenable groups ⋮ Complete Bredon cohomology and its applications to hierarchically defined groups ⋮ Euler classes and Bredon cohomology for groups with restricted families of finite subgroups. ⋮ A note on the Mittag-Leffler condition for Bredon-modules ⋮ Fixed points of finite groups acting on generalised Thompson groups. ⋮ On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups ⋮ Subgroup posets, Bredon cohomology and equivariant Euler characteristics ⋮ Vanishing simplicial volume for certain affine manifolds ⋮ Entropy, determinants, and $L^2$-torsion ⋮ ON THE DIMENSION OF GROUPS THAT SATISFY CERTAIN CONDITIONS ON THEIR FINITE SUBGROUPS

Cites Work

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• On the Cohomological Dimension of Soluble Groups
• Valuations and Finitely Presented Metabelian Groups
• Soluble Groups of Type (FP)∞ have Finite Torsion-Free Rank

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