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 Z 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.
Chirivi, R., Spreafico, M. (2018). Space forms and group resolutions: The tetrahedral family. JOURNAL OF ALGEBRA, 510, 52-97 [10.1016/j.jalgebra.2018.06.004].
Space forms and group resolutions: The tetrahedral family
Spreafico M.
2018
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 Z 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.
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