### The exponent of the homotopy groups of Moore spectra and the stable Hurewicz homomorphism, by Dominique Arlettaz

This paper shows that, for any positive integer n, the order of the
(n+1)-dimensional Postnikov k-invariant of the Moore spectrum associated with
any abelian group G is equal to the exponent of its n-th homotopy group. In
the case of the sphere spectrum S, this implies that the exponents of the
homotopy groups of S provide a universal estimate for the exponent of the
kernel of the stable Hurewicz homomorphism relating the homotopy groups of a
bounded below spectrum X to its E-homology groups, for any connective ring
spectrum E such that its 0-th homotopy group is torsion-free. Moreover, an
upper bound for the exponent of the cokernel of the generalized Hurewicz
homomorphism between the E-homology groups of X and the ordinary homology
groups of X with coefficient in the 0-th homotopy group of E is obtained for
any connective spectrum E. An application of these results enables us to
approximate in a universal way both kernel and cokernel of the unstable
Hurewicz homomorphism between the algebraic K-theory of any ring and the
ordinary integral homology of its linear group.

Dominique Arlettaz <dominique.arlettaz@ima.unil.ch>