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Proceedings of the American Mathematical Society

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



Higher order homology operations and the Adams spectral sequence

Author: Warren M. Krueger
Journal: Proc. Amer. Math. Soc. 27 (1971), 395-398
MSC: Primary 55.52
MathSciNet review: 0281210
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Abstract: One can filter the stable homotopy groups of spheres in such a way as to obtain the (semisimplicial) $ \bmod - p$ Adams spectral sequence and also by means of certain higher order homology operations. In this note we show that these filtrations coincide.

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  • [1] J. F. Adams, On the structure and applications of the Steenrod algebra, Comment. Math. Helv. 32 (1958), 180-204. MR 20 #2711. MR 0096219 (20:2711)
  • [2] A. K. Bousfield, et al, The $ \bmod-p$ lower central series and the Adams spectral sequence, Topology 5 (1966), 331-342. MR 33 #8002. MR 0199862 (33:8002)
  • [3] D. M. Kan and G. W. Whitehead, Orientability and Poincaré duality in general homology theories, Topology 3 (1965), 231-270. MR 32 #8335. MR 0190925 (32:8335)

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Keywords: Semisimplicial spectrum, Adams spectral sequence, $ P$-system, homology operation, universal homology operation, $ n$-step nilpotent spectrum, $ n$-step metabelian spectrum
Article copyright: © Copyright 1971 American Mathematical Society

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