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1999 | 161 | 1-2 | 17-35
Tytuł artykułu

Postnikov invariants of H-spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is known that the order of all Postnikov k-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the k-invariants $k^{m+1}(X)$ of X in dimensions m ≤ 2n if X is an (n-1)-connected H-space which is not necessarily of finite type (n ≥ 1). Similar results hold more generally for higher k-invariants if X is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of X.
Słowa kluczowe
Rocznik
Tom
161
Numer
1-2
Strony
17-35
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-12-15
poprawiono
1998-07-08
Twórcy
  • Max-Planck-Institut für Mathematik, D-53072 Bonn, Germany, npointet@datacomm.ch
  • Zelgstrasse 44, CH-8134 Adliswil, Switzerland
Bibliografia
  • [AC] M. Arkowitz and C. Curjel, The Hurewicz homomorphism and finite homotopy invariants, Trans. Amer. Math. Soc. 110 (1964), 538-551.
  • [A1] D. Arlettaz, On the homology of the special linear group over a number field, Comment. Math. Helv. 61 (1986), 556-564.
  • [A2] D. Arlettaz, On the k-invariants of iterated loop spaces, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 343-350.
  • [A3] D. Arlettaz, The first k-invariant of a double loop space is trivial, Arch. Math. (Basel) 54 (1990), 84-92.
  • [A4] D. Arlettaz, Universal bounds for the exponent of stable homotopy groups, Topology Appl. 38 (1991), 255-261.
  • [A5] D. Arlettaz, Exponents for extraordinary homology groups, Comment. Math. Helv. 68 (1993), 653-672.
  • [C] H. Cartan, Algèbres d'Eilenberg-MacLane et homotopie, Séminaire H. Cartan Ecole Norm. Sup. (1954/1955), exp. 11; see also: Oeuvres, Vol. III, Springer, 1979, 1374-1394.
  • [J] I. M. James, Reduced product spaces, Ann. of Math. (2) 62 (1955), 170-197.
  • [P1] N. Pointet-Tischler, Invariants de Postnikov des espaces de lacets, thèse, Université de Lausanne, 1996.
  • [P2] N. Pointet-Tischler, La suspension cohomologique des espaces d'Eilenberg-MacLane, C. R. Acad. Sci. Paris Sér. I 325 (1997), 1113-1116.
  • [Sm] L. Smith, On the relation between spherical and primitive homology classes in topological groups, Topology 8 (1969), 69-88.
  • [So] C. Soulé, Opérations en K-théorie algébrique, Canad. J. Math. 37 (1985), 488-550.
  • [T] R. Thom, L'homologie des espaces fonctionnels, in: Colloque de topologie algébrique (Louvain, 1956), Masson, 1957, 29-39.
  • [WG1] G. Whitehead, On spaces with vanishing low-dimensional homotopy groups, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 207-211.
  • [WG2] G. Whitehead, Elements of Homotopy Theory, Grad. Texts in Math. 61, Springer, 1978.
  • [WH] J. H. C. Whitehead, A certain exact sequence, Ann. of Math. (2) 52 (1950), 51-110.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv161i1p17bwm
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