Fundamental Domain and Cellular Decomposition of Tetrahedral Spherical Space Forms

Given a free isometric action of the binary tetrahedral group on a (4n − 1)-dimensional sphere, we obtain an explicit finite cellular decomposition of the sphere, equivariant with respect to the group action. A cell decomposition of the correspondent spherical space form and an explicit description...

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Bibliographic Details
Published inCommunications in algebra Vol. 44; no. 2; pp. 768 - 786
Main Authors Fêmina, L. L., Galves, A. P. T., Manzoli Neto, O., Spreafico, M.
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.02.2016
Subjects
Binary tetrahedral group
Cellular decomposition
Fundamental domain
Spherical space forms
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Summary:Given a free isometric action of the binary tetrahedral group on a (4n − 1)-dimensional sphere, we obtain an explicit finite cellular decomposition of the sphere, equivariant with respect to the group action. A cell decomposition of the correspondent spherical space form and an explicit description of the associated cellular chain complex of modules over the integral group ring of the fundamental group of the space form follows. In particular, the construction provides a simple explicit 4-periodic free resolution for the binary tetrahedral group.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2014.990022