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Spherical Space Forms: Homotopy Types and Self-Equivalences for the Group (ℤ/a ⋊ ℤ/b) × SL2 (
p)
Published online by Cambridge University Press: 20 November 2018
Abstract
Let $G=\left( \mathbb{Z}/a\rtimes \mathbb{Z}/b \right)\times \text{S}{{\text{L}}_{2}}\left( {{\mathbb{F}}_{p}} \right)$, and let
$X\left( n \right)$ be an
$n$-dimensional
$CW$-complex of the homotopy type of an
$n$-sphere. We study the automorphism group
$\text{Aut}\left( G \right)$ in order to compute the number of distinct homotopy types of spherical space forms with respect to free and cellular
$G$-actions on all
$CW$-complexes
$X\left( 2dn-1 \right)$, where
$2d$ is the period of
$G$. The groups
$\varepsilon \left( X\left( 2dn-1 \right)/\mu \right)$ of self homotopy equivalences of space forms
$X\left( 2dn-1 \right)/\mu$ associated with free and cellular
$G$-actions
$\mu$ on
$X\left( 2dn-1 \right)$ are determined as well.
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- Copyright
- Copyright © Canadian Mathematical Society 2007
References
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