Abstract.
It is shown that every H \( \frak {F} \)-group G of type \( \rm{FP}_\infty \) admits a finite dimensional G-CW-complex X with finite stabilizers and with the additional property that for each finite subgroup H, the fixed point subspace X H is contractible. This establishes conjecture (5.1.2) of [9]. The construction of X involves joining a family of spaces parametrized by the poset of non-trivial finite subgroups of G and ultimately relies on the theorem of Cornick and Kropholler that if M is a \( \Bbb {Z} G \)-module which is projective as a \( \Bbb {Z} H \)-module for all finite \( H \le G \) then M has finite projective dimension.
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Received: April 30, 1997
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Kropholler, P., Mislin, G. Groups acting on finite dimensional spaces with finite stabilizers. Comment. Math. Helv. 73, 122–136 (1998). https://doi.org/10.1007/s000140050048
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DOI: https://doi.org/10.1007/s000140050048