Uncountably many groups of type $FP$

Abstract

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, ${\ell }^2$- and compactly-supported cohomology of these groups. For each $n\ge 4$ we construct a closed aspherical $n$-manifold that admits an uncountable family of acyclic regular coverings with non-isomorphic covering groups.

Second version 35 pages. Minor improvements to exposition, removal of misprints etc. Third version also 35 pages, one reference added, more misprints removed. Fourth version identical to third version, except that the Theorem numbering is now by Section

References in corpus (1)

• Subgroups of almost finitely presented groups

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