Postnikov invariants of H-spaces

Dominique Arlettaz; Nicole Pointet-Tischler

Fundamenta Mathematicae (1999)

  • Volume: 161, Issue: 1-2, page 17-35
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Arlettaz, Dominique, and Pointet-Tischler, Nicole. "Postnikov invariants of H-spaces." Fundamenta Mathematicae 161.1-2 (1999): 17-35. <http://eudml.org/doc/212399>.

@article{Arlettaz1999,
abstract = {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.},
author = {Arlettaz, Dominique, Pointet-Tischler, Nicole},
journal = {Fundamenta Mathematicae},
keywords = {iterated loop spaces; Hurewicz homomorphism; -invariants},
language = {eng},
number = {1-2},
pages = {17-35},
title = {Postnikov invariants of H-spaces},
url = {http://eudml.org/doc/212399},
volume = {161},
year = {1999},
}

TY - JOUR
AU - Arlettaz, Dominique
AU - Pointet-Tischler, Nicole
TI - Postnikov invariants of H-spaces
JO - Fundamenta Mathematicae
PY - 1999
VL - 161
IS - 1-2
SP - 17
EP - 35
AB - 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.
LA - eng
KW - iterated loop spaces; Hurewicz homomorphism; -invariants
UR - http://eudml.org/doc/212399
ER -

References

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  10. [P2] N. Pointet-Tischler, La suspension cohomologique des espaces d'Eilenberg-MacLane, C. R. Acad. Sci. Paris Sér. I 325 (1997), 1113-1116. Zbl0897.55007
  11. [Sm] L. Smith, On the relation between spherical and primitive homology classes in topological groups, Topology 8 (1969), 69-88. 
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  13. [T] R. Thom, L'homologie des espaces fonctionnels, in: Colloque de topologie algébrique (Louvain, 1956), Masson, 1957, 29-39. 
  14. [WG1] G. Whitehead, On spaces with vanishing low-dimensional homotopy groups, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 207-211. Zbl0031.28601
  15. [WG2] G. Whitehead, Elements of Homotopy Theory, Grad. Texts in Math. 61, Springer, 1978. 
  16. [WH] J. H. C. Whitehead, A certain exact sequence, Ann. of Math. (2) 52 (1950), 51-110. 

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