Large and small group homology

Michael Brunnbauer; Bernhard Hanke

doi:10.1112/jtopol/jtq014

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arXiv · 0902.0869

Large and small group homology

Michael Brunnbauer·Bernhard Hanke

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Abstract

For several instances of metric largeness like enlargeability or having hyperspherical universal covers, we construct non-large vector subspaces in the rational homology of finitely generated groups. The functorial properties of this construction imply that the corresponding largeness properties of closed manifolds depend only on the image of their fundamental classes under the classifying map. This is applied to construct examples of essential manifolds whose universal covers are not hyperspherical, thus answering a question of Gromov (1986), and, more generally, essential manifolds which are not enlargeable.

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Michael Brunnbauer, Bernhard Hanke. 2009-12-04. Large and small group homology. https://doi.org/10.1112/jtopol%2Fjtq014

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