The generalized Boardman homomorphisms

• Autorzy: Dominique Arlettaz
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Boardman homomorphism; cohomotopy groups; generalized cohomology theories; Primary: 55 N 20; 55 Q 55; Secondary: 55 Q 45; 55 S 45

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 1
• Strony: 50-56

Daty

wydano

2004-03-01

online

2004-03-01

Twórcy

autor

Dominique Arlettaz

• Université de Lausanne

Bibliografia

• [1] J.F. Adams: Stable homotopy and generalised homology, The University of Chicago Press, Chicago, 1974.
• [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
• [3] D. Arlettaz: “Exponents for extraordinary homology groups”, Comment. Math. Helv., Vol. 68, (1993), pp. 653–672.
• [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.
• [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
• [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

Identyfikatory

DOI

10.2478/BF02475949