Abstract view
Spherical Space Forms: Homotopy Types and SelfEquivalences for the Group $({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times SL_2\,(\mathbb{F}_p)$


Published:20070601
Printed: Jun 2007
Marek Golasiński
Daciberg Lima Gonçalves
Abstract
Let $G=({\mathbb Z}/a\rtimes{\mathbb Z}/b) \times
\SL_2(\mathbb{F}_p)$, and let $X(n)$ be an $n$dimensional
$CW$complex of the homotopy type of an $n$sphere. We study the
automorphism group $\Aut (G)$ 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 $X(2dn1)$, where $2d$
is the period of $G$. The groups ${\mathcal E}(X(2dn1)/\mu)$ of self
homotopy equivalences of space forms $X(2dn1)/\mu$ associated with
free and cellular $G$actions $\mu$ on $X(2dn1)$ are determined as
well.
Keywords: 
automorphism group, $CW$complex, free and cellular $G$action, group of self homotopy equivalences, LyndonHochschildSerre spectral sequence, special (linear) group, spherical space form
automorphism group, $CW$complex, free and cellular $G$action, group of self homotopy equivalences, LyndonHochschildSerre spectral sequence, special (linear) group, spherical space form
