Homotopy nilpotency of localized spheres and projective spaces
Homotopy nilpotency of localized spheres and projective spaces
Abstract For the $p$ -localized sphere $\mathbb {S}^{2m-1}_{(p)}$ with $p >3$ a prime, we prove that the homotopy nilpotency satisfies $\mbox {nil}\ \mathbb {S}^{2m-1}_{(p)}<\infty$ , with respect to any homotopy associative $H$ -structure on $\mathbb {S}^{2m-1}_{(p)}$ . We also prove that $\mbox {nil}\ \mathbb {S}^{2m-1}_{(p)}= 1$ for all but a …