Fringe families in stable homotopy

Zahler, Raphael S.

doi:10.1090/S0002-9947-1976-0431160-5

Fringe families in stable homotopy
HTML articles powered by AMS MathViewer

by Raphael S. Zahler

Trans. Amer. Math. Soc. 224 (1976), 243-253

DOI: https://doi.org/10.1090/S0002-9947-1976-0431160-5

PDF | Request permission

Abstract:

It is shown how to detect and construct elements in the stable homotopy groups of spheres corresponding to the ${_i}$ family of Toda. The only tools used are Brown-Peterson cohomology and the Adams spectral sequence.

References

J. F. Adams, On the groups $J(X)$. IV, Topology 5 (1966), 21–71. MR 198470, DOI 10.1016/0040-9383(66)90004-8
D. C. Johnson, H. R. Miller, W. S. Wilson, and R. S. Zahler, Boundary homomorphisms in the generalized Adams spectral sequence and the nontriviality of infinitely many $\gamma _{t}$ in stable homotopy, Conference on homotopy theory (Evanston, Ill., 1974) Notas Mat. Simpos., vol. 1, Soc. Mat. Mexicana, México, 1975, pp. 47–63. MR 761720

Detecting stable homotopy with secondary cobordism operations

Peter S. Landweber, Annihilator ideals and primitive elements in complex bordism, Illinois J. Math. 17 (1973), 273–284. MR 322874
Haynes R. Miller and W. Stephen Wilson, On Novikov’s Ext1 modulo an invariant prime ideal, Topology 15 (1976), no. 2, 131–141. MR 433434, DOI 10.1016/0040-9383(76)90002-1
S. P. Novikov, Methods of algebraic topology from the point of view of cobordism theory, Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 855–951 (Russian). MR 0221509
Shichirô Oka, A new family in the stable homotopy groups of spheres, Hiroshima Math. J. 5 (1975), 87–114. MR 380791
Larry Smith, On realizing complex bordism modules. Applications to the stable homotopy of spheres, Amer. J. Math. 92 (1970), 793–856. MR 275429, DOI 10.2307/2373397
Larry Smith, On realizing complex bordism modules. Applications to the stable homotopy of spheres, Amer. J. Math. 92 (1970), 793–856. MR 275429, DOI 10.2307/2373397

On realizing complex bordism modules

Hirosi Toda, $p$-primary components of homotopy groups. IV. Compositions and toric constructions, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 32 (1959), 297–332. MR 111041, DOI 10.1215/kjm/1250776579
Hirosi Toda, On spectra realizing exterior parts of the Steenrod algebra, Topology 10 (1971), 53–65. MR 271933, DOI 10.1016/0040-9383(71)90017-6
Emery Thomas and Raphael Zahler, Generalized higher order cohomology operations and stable homotopy groups of spheres, Advances in Math. 20 (1976), no. 3, 287–328. MR 423351, DOI 10.1016/0001-8708(76)90200-0
Raphael Zahler, The Adams-Novikov spectral sequence for the spheres, Ann. of Math. (2) 96 (1972), 480–504. MR 319197, DOI 10.2307/1970821
Raphael Zahler, Detecting stable homotopy with secondary cobordism operations. I, Quart. J. Math. Oxford Ser. (2) 25 (1974), 213–226. MR 367998, DOI 10.1093/qmath/25.1.213
Raphael S. Zahler, Nonrealizability of some cyclic complex bordism modules, Proc. Amer. Math. Soc. 47 (1975), 218–222. MR 362306, DOI 10.1090/S0002-9939-1975-0362306-X