Spherical space forms - Homotopy self-equivalences and homotopy types,the case of the groups Z/α × (Z/b × TL_2(F_p))

摘要

Let G = Z/a ×_μ (Z/b × TL_2(F_p)) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group ε(X(2dn - 1)/α) of homotopy self-equivalences of spherical space forms X(2dn - 1)/α associated with such G-actions α on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction.