# 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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