Journal of the Mathematical Society of Japan

The Gottlieb group of a wedge of suspensions

Martin ARKOWITZ and Ken-ichi MARUYAMA

Full-text: Open access

Abstract

We study the Gottlieb group of a wedge sum of suspension spaces. We give necessary and sufficient conditions, in terms of Hopf invariants, for an element of a homotopy group to be in the Gottlieb group. We apply our results to wedge sums of spheres and to Moore spaces.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 3 (2014), 735-743.

Dates
First available in Project Euclid: 24 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1406206970

Digital Object Identifier
doi:10.2969/jmsj/06630735

Mathematical Reviews number (MathSciNet)
MR3238315

Zentralblatt MATH identifier
1314.55009

Subjects
Primary: 55Q20: Homotopy groups of wedges, joins, and simple spaces
Secondary: 55Q25: Hopf invariants

Keywords
homotopy groups Gottlieb groups wedge sums Hopf invariants Whitehead products

Citation

ARKOWITZ, Martin; MARUYAMA, Ken-ichi. The Gottlieb group of a wedge of suspensions. J. Math. Soc. Japan 66 (2014), no. 3, 735--743. doi:10.2969/jmsj/06630735. https://projecteuclid.org/euclid.jmsj/1406206970


Export citation

References

  • M. Arkowitz, The generalized Whitehead product, Pacific J. Math., 12 (1962), 7–23.
  • W. D. Barcus and M. G. Barratt, On the homotopy classification of the extensions of a fixed map, Trans. Amer. Math. Soc., 88 (1958), 57–74.
  • Y. Félix, S. Halperin and J.-C. Thomas, Rational Homotopy Theory, Grad. Texts in Math., 205, Springer-Verlag, 2001.
  • M. Golasiński and J. Mukai, Gottlieb groups of spheres, Topology, 47 (2008), 399–430.
  • D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math., 91 (1969), 729–756.
  • P. J. Hilton, On the homotopy groups of the union of spheres, J. London Math. Soc., 30 (1955), 154–171.
  • H. Toda, Composition Methods in Homotopy Groups of Spheres, Ann. of Math. Stud., 49, Princeton University Press, Princeton, N.J., 1962.
  • G. W. Whitehead, Elements of Homotopy Theory, Grad. Texts in Math., 61, Springer-Verlag, 1978.