Cellular decomposition and free resolution for split metacyclic spherical space forms

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 c...

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Bibliographic Details
Published inHomology, homotopy, and applications Vol. 15; no. 1; pp. 253 - 278
Main Authors Fêmina, L.L., Galves, A.P.T., Neto, O. Manzoli, Spreafico, M.
Format Journal Article
LanguageEnglish
Published International Press of Boston 2013
Subjects
16E05
18G10
20J05
20J06
57M07
57M10
57Q10
fundamental domain
Metacyclic group
spherical space form
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Summary: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.
ISSN:1532-0073
1532-0081
DOI:10.4310/HHA.2013.v15.n1.a13