Geodesic
The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism
Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 483-495

Voir la notice de l'article provenant de la source Cambridge University Press

This paper shows that for the Moore spectrum MG associated with any abelian group G, and for any positive integer n, the order of the Postnikov k-invariant k n+1(MG) is equal to the exponent of the homotopy group πnMG. 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 hn : πnX → En (X) for the homology theory E *(—) corresponding to any connective ring spectrum E such that π 0 E is torsion-free and for any bounded below spectrum X. Moreover, an upper bound for the exponent of the cokernel of the generalized Hurewicz homomorphism hn : En (X) → Hn (X; π 0 E), induced by the 0-th Postnikov section 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.
DOI : 10.4153/CJM-1996-024-3
Mots-clés : 55N20, 55P42, 19D55, 55Q45, 55S45 
Arlettaz, Dominique. The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism. Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 483-495. doi: 10.4153/CJM-1996-024-3
@article{10_4153_CJM_1996_024_3,
     author = {Arlettaz, Dominique},
     title = {The {Exponent} of the {Homotopy} {Groups} of {Moore} {Spectra} and the {Stable} {Hurewicz} {Homomorphism}},
     journal = {Canadian journal of mathematics},
     pages = {483--495},
     year = {1996},
     volume = {48},
     number = {3},
     doi = {10.4153/CJM-1996-024-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-024-3/}
}
TY  - JOUR
AU  - Arlettaz, Dominique
TI  - The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 483
EP  - 495
VL  - 48
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-024-3/
DO  - 10.4153/CJM-1996-024-3
ID  - 10_4153_CJM_1996_024_3
ER  - 
%0 Journal Article
%A Arlettaz, Dominique
%T The Exponent of the Homotopy Groups of Moore Spectra and the Stable Hurewicz Homomorphism
%J Canadian journal of mathematics
%D 1996
%P 483-495
%V 48
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-024-3/
%R 10.4153/CJM-1996-024-3
%F 10_4153_CJM_1996_024_3

[1] 1. Adams, J.E., Stable homotopy and generalised homology, The University of Chicago Press, 1974. Google Scholar

[2] 2. Arlettaz, D., The Hurewicz homomorphism in algebraic K-theory, J. Pure Appl. Algebra 71 (1991), 1–12. Google Scholar

[3] 3. Arlettaz, D., The order of the differentials in the Atiyah-Hirzebruch spectral sequence, k-Theory 6 (1992), 347–361. Google Scholar

[4] 4. Arlettaz, D., Exponents for extraordinary homology groups, Comment. Math. Helv. 68 (1993), 653–672. Google Scholar

[5] 5. Borel, A., Cohomologie réelle stable de groupes S-arithmétiques classiques, C. R. Acad. Sci. Paris Ser. A 274 (1972), 1700–1702. Google Scholar

[6] 6. Sah, C.H., Homology of classical groups made discrete III, J. Pure Appl. Algebra 56 (1989), 269–312. Google Scholar

[7] 7. Scherer, J., Exponents for high-dimensional Gamma groups, Exposition. Math. 13 (1995), 455–468. Google Scholar

[8] 8. Suslin, A.A., Homology of GLn, characteristic classes andMilnor K-theory, in Algebraic K-theory, number theory, geometry and analysis, Lecture Notes in Math., Springer 1046 (1984), 357–375. Google Scholar

[9] 9. Switzer, R.M., Algebraic topology - homotopy and homology, Die Grundlehren der mathematischen Wissenschaften, Springer 212 (1975). Google Scholar

[10] 10. Vick, J.W., Poincare duality and Postnikov factors, Rocky Mountain J. Math 3 (1973), 483–499. Google Scholar

Cité par Sources :