Uncountably many groups of type FP

@article{Leary2015UncountablyMG,
  title={Uncountably many groups of type FP},
  author={Ian J. Leary},
  journal={Proceedings of the London Mathematical Society},
  year={2015},
  volume={117}
}
  • I. Leary
  • Published 21 December 2015
  • Mathematics
  • Proceedings of the London Mathematical Society
We construct uncountably many discrete groups of type FP; in particular we construct groups of type FP that do not embed in any finitely presented group. We compute the ordinary, ℓ2 , and compactly supported cohomology of these groups. For each n⩾4 we construct a closed aspherical n ‐manifold that admits an uncountable family of acyclic regular coverings with non‐isomorphic covering groups. 
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