ON FINITE GROUPS ACTING ON ACYCLIC COMPLEXES OF DIMENSION TWO Abstract

We conjecture that every finite group C acting on a contractible CW-complex X of dimension 2 has at least one fixed point. We prove this in the case where C is solvable, and under this additional hypothesis, the result holds for X acyclic. Let G be a group and A an abelian group. Dicks and Dunwoody ([4, Chapter IV]) proved that for each element ( of H1 (G; AG) there exists a G-tree T with finite edge stabilizers, with the property that for each subgroup H of G, the restriction of ( to H is zero if and only if