Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Higher $ p$-torsion in the $ \beta$-family


Author: Hal Sadofsky
Journal: Proc. Amer. Math. Soc. 108 (1990), 1063-1071
MSC: Primary 55Q10; Secondary 55Q40, 55T15
DOI: https://doi.org/10.1090/S0002-9939-1990-0994790-0
MathSciNet review: 994790
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the existence of new families of $ {\upsilon _2}$-periodic elements of the stable homotopy of the sphere detected in the second filtration of the Adams-Novikov Spectral Sequence for primes greater than 3. Our main corollary is that the $ p$-component of $ \pi _ * ^s$ contains any finite abelian $ p$-group as a subgroup in some dimension $ ({\text{for}}p \geq 5)$.


References [Enhancements On Off] (What's this?)

  • [1] Lin Jinkun, Detection of second periodicity families in stable homotopy of spheres, (not yet published).
  • [2] Haynes R. Miller, Douglas C. Ravenel, and W. Stephen Wilson, Periodic phenomena in the Adams-Novikov spectral sequence. Ann. of Math. 106 (1977), 469-516. MR 0458423 (56:16626)
  • [3] Shichiro Oka, Small ring spectra and the $ p$-rank of the stable homotopy of spheres, Proceedings of the 1982 Northwestern Conference in Homotopy Theory, Contemp. Math. 19, Amer. Math. Soc., (1983), 267-308. MR 711058 (84j:55006)
  • [4] -, Derivations in ring spectra and higher torsions in coker $ J$, Memoirs of the Faculty of Science, Kyushu University Ser. A, Vol. 38, No. 1, 1984, 23-46. MR 736944 (85h:55019)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55Q10, 55Q40, 55T15

Retrieve articles in all journals with MSC: 55Q10, 55Q40, 55T15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-0994790-0
Keywords: Beta-family, Adams-Novikov Spectral Sequence, stable homotopy groups of spheres, split ring spectrum
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society