An algebraic analogue of a conjecture of G. W. Whitehead
HTML articles powered by AMS MathViewer
- by Haynes Miller PDF
- Proc. Amer. Math. Soc. 84 (1982), 131-137 Request permission
Abstract:
Using a theorem of W. M. Singer, an algebraic analogue of a conjecture of G. W. Whitehead is proved, generalizing the algebraic Kahn-Priddy theorem of W. H. Lin.References
- José Adem, The relations on Steenrod powers of cohomology classes. Algebraic geometry and topology, A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N.J., 1957, pp. 191–238. MR 0085502
- Donald W. Anderson and Donald M. Davis, A vanishing theorem in homological algebra, Comment. Math. Helv. 48 (1973), 318–327. MR 334207, DOI 10.1007/BF02566125
- Albrecht Dold and René Thom, Quasifaserungen und unendliche symmetrische Produkte, Ann. of Math. (2) 67 (1958), 239–281 (German). MR 97062, DOI 10.2307/1970005
- I. M. James, Emery Thomas, H. Toda, and G. W. Whitehead, On the symmetric square of a sphere, J. Math. Mech. 12 (1963), 771–776. MR 0154282
- Daniel S. Kahn and Stewart B. Priddy, On the transfer in the homology of symmetric groups, Math. Proc. Cambridge Philos. Soc. 83 (1978), no. 1, 91–101. MR 464229, DOI 10.1017/S0305004100054323
- W. H. Lin, D. M. Davis, M. E. Mahowald, and J. F. Adams, Calculation of Lin’s Ext groups, Math. Proc. Cambridge Philos. Soc. 87 (1980), no. 3, 459–469. MR 569195, DOI 10.1017/S0305004100056899
- Wen Hsiung Lin, The algebraic Kahn-Priddy theorem, Bull. London Math. Soc. 13 (1981), no. 3, 239–240. MR 614662, DOI 10.1112/blms/13.3.239
- R. James Milgram (ed.), Problems presented to the 1970 AMS Summer Colloquium in Algebraic Topology, Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 187–201. MR 0315691
- Haynes Miller, A spectral sequence for the homology of an infinite delooping, Pacific J. Math. 79 (1978), no. 1, 139–155. MR 526673
- Haynes Miller and Clarence Wilkerson, Vanishing lines for modules over the Steenrod algebra, J. Pure Appl. Algebra 22 (1981), no. 3, 293–307. MR 629336, DOI 10.1016/0022-4049(81)90104-3
- Minoru Nakaoka, Cohomology mod $p$ of the $p$-fold symmetric products of spheres, J. Math. Soc. Japan 9 (1957), 417–427. MR 121787, DOI 10.2969/jmsj/00940417 W. M. Singer, An embedding theorem for the homology of the Steenrod algebra (to appear).
- Peter J. Welcher, Symmetric products and the stable Hurewicz homomorphism, Illinois J. Math. 24 (1980), no. 4, 527–544. MR 586793 —, Symmetric fiber spectra and $K(n)$-homology acyclicity, Indiana Univ. Math. J. (to appear).
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 131-137
- MSC: Primary 55T15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633294-7
- MathSciNet review: 633294