Some remarks on group actions on hyperbolic 3-manifolds

Abstract

We prove that there are infinitely many non-commensurable closed orientable hyperbolic 3-manifolds X, with the property that there are finite groups G1 and G2 acting freely by orientation-preserving isometries on X with X/G1 and X/G2 isometric, but G1 and G2 are not conjugate in Isom(X). We provide examples where G1 and G2 are non-isomorphic, and prove analogous results when G1 and G2 act with fixed-points. Dedicated to Marston Conder on the occasion of his 65th birthday