The generalized Boardman homomorphisms
Dominique Arlettaz
Open Mathematics, Tome 2 (2004), p. 50-56 / Harvested from The Polish Digital Mathematics Library
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This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism b n: π n(X)→H n(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π n(X)→E n(X), F n(X)→(E∧F)n(X), F n(X)→H n(X;π 0 F) and F n(X)→H n+t(X;π t F) for other cohomology theories E *(−) and F *(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in terms of the order of the Postnikov invariants of the spectrum F.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:268736 
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     author = {Dominique Arlettaz},
     title = {The generalized Boardman homomorphisms},
     journal = {Open Mathematics},
     volume = {2},
     year = {2004},
     pages = {50-56},
     zbl = {1047.55007},
     language = {en},
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Dominique Arlettaz. The generalized Boardman homomorphisms. Open Mathematics, Tome 2 (2004) pp. 50-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475949/

[1] J.F. Adams: Stable homotopy and generalised homology, The University of Chicago Press, Chicago, 1974. | Zbl 0309.55016

[2] D. Arlettaz: “The order of the differentials in the Atiyah-Hirzebruch spectral sequence”, K-Theory, Vol. 6, (1992), pp. 347–361. http://dx.doi.org/10.1007/BF00966117 | Zbl 0768.55012

[3] D. Arlettaz: “Exponents for extraordinary homology groups”, Comment. Math. Helv., Vol. 68, (1993), pp. 653–672. | Zbl 0968.55003

[4] D. Arlettaz: “The exponent of the homotopy groups of Moore spectra and the stable Hurewicz homomorphism”, Canad. J. Math., Vol. 48, (1996), pp. 483–495. | Zbl 0866.55003

[5] C.R.F. Maunder: “The spectral sequence of an extraordinary cohomology theory”, Math. Proc. Cambridge Philos. Soc., Vol. 59, (1963), pp. 567–574 http://dx.doi.org/10.1017/S0305004100037245 | Zbl 0116.14603

[6] R.M. Switzer: Algebraic topology-homotopy and homology, Die Grundlehren der mathematischen Wissenschaften, 1975.

[7] J.W. Vick: “Poincaré duality and Postnikov factors”, Rocky Mountain J. Math., Vol. 3, (1973), pp. 483–499 http://dx.doi.org/10.1216/RMJ-1973-3-3-483 | Zbl 0272.55011