Free Actions of Generalized Quaternion Groups on Spheres

On the $K$-ring of the classifying space of the generalized quaternion group

“…The K -ring of the classifying space BQ 2 n of the generalized quaternion group Q 2 n , n ≥ 3, is described classically in [4] and [7]. In this note, we describe these rings in a simpler way, by a minimal set of relations on a minimal set of generators.…”

“…the K -order of the main vector bundle over the corresponding spherical forms, in a much shorter way than is done in [7].…”

“…The reader may find more about the geometric meaning of these orders and quaternionic spherical forms in [4] and [7].…”

On Stable Homotopy Types of Some Stunted Spaces

“…In this section we examine the representation groups of the generalized quaternion groups D*(2 m+1 ) according to Pitt [19].…”

Nonimmersions and nonembeddings of quaternionic spherical space forms

“…The quotient manifold S4"+3/Qk is called the quaternionic spherical space form. D. Pitt [8] studied the structure of K-and KO-nngs of S4"+3/Qk and considered the problem of immersing or embedding S4n+3/Qk in Euclidean space Rm using the techniques of M. F. Atiyah [1] (cf. also [5,Chapter 6] and [6,Chapter …”