Homology, Homotopy and Applications
Volume 15 (2013)
Cellular decomposition and free resolution for split metacyclic spherical space forms
Pages: 253 – 278
Given a free isometric action of a split metacyclic group on odd dimensional sphere, we obtain an explicit finite cellular decomposition of the sphere equivariant with respect to the group action. A cell decomposition of the factor space and an explicit description of the associated cellular chain complex of modules over the integral group ring of the fundamental group follow. In particular, the construction provides a simple explicit 4-periodic free resolution for the split metacyclic groups.
metacyclic group, fundamental domain, spherical space form
2010 Mathematics Subject Classification
16E05, 18G10, 20J05, 20J06, 57M07, 57M10, 57Q10