The qsf property and group actions via complexes of spaces (Q1266197)

A locally compact space \(P\) is called quasi simply filtrated (qsf) if any compact subset \(C\subset P\) admits an extension \(f:A\to P\) from a 1-connected compact space \(A\). A finitely presented group acting freely and cocompactly on a 1-connected qsf space is called qsf itself, and this was shown to be a group-theoretic property by \textit{S. G. Brick} and \textit{M. L. Mihalik} [Math. Z. 220, No. 2, 207-217 (1995; Zbl 0843.57003)]. Using the machinery known as a complex of spaces, the authors develop the relationship between qsf complexes and the qsf condition on groups which act on them. Amongst other results they show, that one obtains the same groups if one replaces ``freely'' with ``properly discontinuous'' in the definition of a qsf group. In particular, groups acting properly discontinuously and cocompactly on a locally finite building are qsf; and so are cocompact Fuchsian and Kleinian groups.