Homology, Homotopy and Applications

Cellular decomposition and free resolution for split metacyclic spherical space forms

L. L. Fêmina, A. P. T. Galves, O. Manzoli Neto, and M. Spreafico

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Abstract

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.

Article information

Source
Homology Homotopy Appl., Volume 15, Number 1 (2013), 253-278.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hha/1383943677

Mathematical Reviews number (MathSciNet)
MR3079207

Zentralblatt MATH identifier
1276.57037

Subjects
Primary: 57M07: Topological methods in group theory 57M10: Covering spaces 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28] 16E05: Syzygies, resolutions, complexes 18G10: Resolutions; derived functors [See also 13D02, 16E05, 18E25] 20J05: Homological methods in group theory 20J06: Cohomology of groups

Keywords
Metacyclic group fundamental domain spherical space form

Citation

Fêmina, L. L.; Galves, A. P. T.; Neto, O. Manzoli; Spreafico, M. Cellular decomposition and free resolution for split metacyclic spherical space forms. Homology Homotopy Appl. 15 (2013), no. 1, 253--278. https://projecteuclid.org/euclid.hha/1383943677


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