Space Forms and Group Resolutions: the tetrahedral family

Abstract

The orbit polytope for a finite group G acting linearly and freely on a sphere S is used to construct a cellularized fundamental domain for the action. A resolution of the integers over G results from the associated G-equivariant cellularization of S. This technique is applied to the generalized binary tetrahedral group family; the homology groups, the cohomology rings and the Reidemeister torsions of the related spherical space forms are determined.

37 pages, 5 figures. A proof of the minimal rank property for the resolution has been added