Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T07:24:05.985Z Has data issue: false hasContentIssue false

Some infinite families in the stable homotopy of spheres

Published online by Cambridge University Press:  24 October 2008

Wen-Hsiung Lin
Affiliation:
Department of Mathematics, Tsing Hua University, Taiwan, Republic of China

Extract

The classical Adams spectral sequence [1] has been an important tool in the computation of the stable homotopy groups of spheres . In this paper we make another contribution to this computation.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Adams, J. F.. On the structure and applications of the Steenrod algebra. Gomm. Math. Helv. 32 (1958), 180214.CrossRefGoogle Scholar
[2]Adams, J. F.. On the non-existence of elements of Hopf invariant one. Ann. Math. 72 (1960), 20104.CrossRefGoogle Scholar
[3]Bousfield, A. K., Curtis, E. B., Kan, D. M., Quillen, D. G., Rector, D. L. and Shlessinger, J. W.. The mod-p lower central series and the Adams spectral sequence II. Topology 9 (1970), 309316.Google Scholar
[4] The Adams spectral sequence of Ω2 S3 and Brown–Gitler spectra. To appear on the conference in celebration of J. C. Moore's 60th birthday (1983).Google Scholar
[5]Brown, E. H. Jr. and Peterson, F. P.. The Brown–Gitler spectrum, the space Ω2 S3 and the elements ηj∈π2j(S). Proc. Steklov Inst. Math. 4 (1984), 4145.Google Scholar
[6]Brown, E. H. Jr. and Gitler, S.. A spectrum whose cohomology is a certain cyclic module over the Steenrod algebra. Topology 12 (1973), 283296.Google Scholar
[7]Cohen, R. L. and Goerss, P.. Secondary cohomology operations that detect homotopy classes. Topology 23 (1984), 177194.Google Scholar
[8]Davis, D. M.. An infinite family in the cohomology of the Steenrod algebra. J. Pure Appl. Algebra 21 (1981), 145150.Google Scholar
[9]Lin, W. H., Davis, D. M., Mahowald, M. E. and Adams, J. F.. Calculation of Lin's Ext groups. Math. Proc. Cambridge Philos. Soc. 87 (1980), 459469.Google Scholar
[10]Lin, W. H.. Cohomology of the Steenrod algebra. J. Pure Appl. Algebra 29 (1983), 7592.CrossRefGoogle Scholar
[11]Mahowald, M. E.. A new infinite family in 2π*2. Topology 16 (1977), 249256.CrossRefGoogle Scholar
[12]Mahowald, M. E. and Tangora, M. C.. On secondary operations which detect homotopy classes. Bol. Soc. Mat. Mex. 12 (1967), 7175.Google Scholar
[13]May, J. P.. The cohomology of restricted Lie algebras and of Hopf algebras. J. Algebra 3 (1966), 123146.CrossRefGoogle Scholar
[14]Wang, J. S. P.. On the cohomology of the mod 2 Steenrod algebra and the non-existence of elements of Hopf invariant one. Illinois J. Math. 11 (1967), 480490.CrossRefGoogle Scholar