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Schmidt, Robert (2020): Coarse homology of leaves of foliations. In: Journal of Topology and Analysis, Vol. 12, No. 4: pp. 1003-1018
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We investigate the coarse homology of leaves in foliations of compact manifolds. This is motivated by the observation that the non-leaves constructed by Schweitzer and by Zeghib all have non-finitely generated coarse homology. This led us to ask whether the coarse homology of leaves in a compact manifold always has to be finitely generated. We show that this is not the case by proving that there exist many leaves with non-finitely generated coarse homology. Moreover, we improve Schweitzer's non-leaf construction and produce non-leaves with trivial coarse homology.