FINITENESS PROPERTIES FOR SOME RATIONAL POINCARE DUALITY GROUPS

摘要

A combination of Bestvina-Brady Morse tneory and an acyclic reflection group trick produces a torsion-free finitely presented Q-Poincare duality group which is not the fundamental group of an aspherical closed ANR Q-homology manifold. The acyclic construction suggests asking which Q-Poincare duality groups act freely on Q-acyclic spaces (i.e., which groups are FH(Q)). For example, the orbifold fundamental group F of a good orbifold satisfies Q-Poincare duality, and we show Γ is FH(Q) if the Euler characteristics of certain fixed sets vanish.