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Calculation of Lin's Ext groups

  • W. H. Lin (a1), D. M. Davis (a2), M. E. Mahowald (a3) and J. F. Adams (a4)

The first-named author has proved interesting results about the stable homotopy and cohomotopy of spaces related to real projective space RP; these are presented in an accompanying paper (6). His proof is by the Adams spectral sequence, and so depends on the calculation of certain Ext groups. The object of this paper is to prove the required result about Ext groups. The proof to be given is not Lin's original proof, which involved substantial calculation; it follows an idea of the second and third authors. The version to be given incorporates modifications suggested later by the fourth author.

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(1)Adams J. F. Operations of the nth kind in K-theory, and what we don't know about RP. London Math. Soc. Lecture Notes no. 11, pp. 19. (Cambridge University Press, 1974).
(2)Atiyah M. F. Thom complexes. Proc. London Math. Soc. (3) 11 (1961), 291310.
(3)Cartan H. and Eilenberg S. Homological Algebra (Princeton University Press, 1956).
(4)Lin T. Y. and Margolis H. R. Homological aspects of modules over the Steenrod algebra. J. Pure and Applied Algebra 9 (1977), 121129.
(5)Lin W. H. The Adams–Mahowald conjecture on real projective spaces. Math. Proc. Cambridge Philos. Soc. 86 (1979), 237241.
(6)Lin W. H. On conjectures of Mahowald, Segal and Sullivan. Math. Proc. Cambridge Philos. Soc. 87 (1980), 449458.
(7)Milnor J. The Steenrod algebra and its dual. Ann. of Math. (2) 67 (1958), 150171.
(8)Milnor J. and Moore J. C. On the structure of Hopf algebras. Ann. of Math. (2) 81 (1965), 211264.
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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