Coarse homology of leaves

Robert Schmidt

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arXiv · 1411.2951

Coarse homology of leaves

Robert Schmidt

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Abstract

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.

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Robert Schmidt. 2014-11-11. Coarse homology of leaves. https://arxiv.org/abs/1411.2951

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