We give a Sobolev inequality characterisation for the vanishing of the fundamental class in the controlled coarse homology of Nowak and Špakula for quasiconvex uniform spaces that support a local weak (1, 1)-Poincaré inequality. Among the applications, we consider visual Gromov hyperbolic spaces.
Cite this article
Juhani Koivisto, Characterising Sobolev inequalities by controlled coarse homology and applications for hyperbolic spaces. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1055–1070DOI 10.4171/RMI/1015