Space Forms and Group Resolutions: the tetrahedral family
Algebraic Topology
2017-10-10 v2
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.
Keywords
Cite
@article{arxiv.1709.03335,
title = {Space Forms and Group Resolutions: the tetrahedral family},
author = {Rocco Chirivi' and Mauro Spreafico},
journal= {arXiv preprint arXiv:1709.03335},
year = {2017}
}
Comments
37 pages, 5 figures. A proof of the minimal rank property for the resolution has been added