Projective resolutions up to bounded torsion and bounds for the orders of the finite subgroups. (Q387603)

Following the paper by \textit{W. Lück} et al., [K-Theory 30, No. 2, 137-165 (2003; Zbl 1053.55004)], an almost-isomorphism of groups is a morphism whose kernel and cokernel are annihilated by certain non-zero integers. In this paper, the authors exploit this notion of almost-isomorphism to develop a homological algebra ``up to bounded torsion''. In particular, they define almost-projective modules, almost-projective resolution, \dots, and they show that the Tor and Ext functors can be computed up to almost-isomorphisms using almost-projective resolutions.