Homotopy types of orbit spaces and their self-equivalences for the periodic groups Z/a \rtimes (Z/b x T^\star_n) and Z/a \rtimes (Z/b x O^\star_n)

Marek Golasinski and Daciberg Lima Goncalves

Let $G$ be a finite group given in one of the forms listed in the title with period $2d$ and $X(n)$ an $n$-dimensional $CW$-complex with the homotopy type of an $n$-sphere. \par We study the automorphism group $\mbox{Aut}\,(G)$ to compute the number of distinct homotopy types of orbit spaces $X(2dn-1)/\mu$ with respect to free and cellular $G$-actions $\mu$ on all $CW$-complexes $X(2dn-1)$. At the end, the groups ${\mathcal E}(X(2dn-1)/\mu)$ of self homotopy equivalences of orbit spaces $X(2dn-1)/\mu$ associated with free and cellular $G$-actions $\mu$ on $X(2dn-1)$ are determined.

Journal of Homotopy and Related Structures, Vol. 1(2006), No. 1, pp. 29-45