Large and small group homology

Details Large and small group homology Large and small group homology

2009-02-05

arxiv.org/abs/0902.0869v2

Mathematics

Geometric Topology

24 pages, small corrections and improvements

Scientific paper

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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