On the suspension order of (Rp(2m))([k])

摘要

It is shown that the suspension order of the k-fold cartesian product (Rp(2m))([k]) of real projective 2m-space Rp(2m) is less than or equal to the suspension order of the k-fold symmetric product (SPRP2m)-R-k of Rp(2m) and greater than or equal to 2(r+s+1), where k and m satisfy 2(r) less than or equal to 2m < 2(r+1) and 2(s) less than or equal to k < 2(s+1). In particular RP2 x RP2 has suspension Order 8, and for fixed m greater than or equal to 1 the suspension orders of the spaces (Rp(2m))([k]) are unbounded while their stable suspension orders are constant and equal to 2(phi(2m)). [References: 9]