Stephen D. Theriault - Homotopy exponents for certain -2r Moore spaces

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Stephen D. Theriault - Homotopy exponents for certain $\mod$ -2^r Moore spaces

STEPHEN D. THERIAULT, Department of Mathematics, MIT, Cambridge, Massachusetts 02139, USA

Homotopy exponents for certain $\mod$ -2^r Moore spaces

For a prime p, the $\mod$ -p^r Moore space P^m(p^r) is the cofiber of the degree p^r map on S^m. A special case of Barratt's conjecture is that if $p^{r}\neq 2$ then the p-primary torsion in $\pi_{\ast}\bigl(P^{m}(p^{r})\bigr)$ is annihilated by p^r+1. It is well known that this is true when p is an odd prime. We investigate to what extent it is true when p=2 and $r\geq 2$ .