Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-17T16:24:44.900Z Has data issue: false hasContentIssue false

Calculation of Lin's Ext groups

Published online by Cambridge University Press:  24 October 2008

W. H. Lin
Affiliation:
National Chengchi University, Taipei, Taiwan.
D. M. Davis
Affiliation:
Lehigh University, Bethlehem, Pa. 18015, USA.
M. E. Mahowald
Affiliation:
Northwestern University, Evanston, Ill. 60201, USA.
J. F. Adams
Affiliation:
DPMMS, 16 Mill Lane, Cambridge CB2 1SB.

Extract

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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(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).Google Scholar
(2)Atiyah, M. F.Thom complexes. Proc. London Math. Soc. (3) 11 (1961), 291310.Google Scholar
(3)Cartan, H. and Eilenberg, S.Homological Algebra (Princeton University Press, 1956).Google Scholar
(4)Lin, T. Y. and Margolis, H. R.Homological aspects of modules over the Steenrod algebra. J. Pure and Applied Algebra 9 (1977), 121129.Google Scholar
(5)Lin, W. H.The Adams–Mahowald conjecture on real projective spaces. Math. Proc. Cambridge Philos. Soc. 86 (1979), 237241.Google Scholar
(6)Lin, W. H.On conjectures of Mahowald, Segal and Sullivan. Math. Proc. Cambridge Philos. Soc. 87 (1980), 449458.Google Scholar
(7)Milnor, J.The Steenrod algebra and its dual. Ann. of Math. (2) 67 (1958), 150171.Google Scholar
(8)Milnor, J. and Moore, J. C.On the structure of Hopf algebras. Ann. of Math. (2) 81 (1965), 211264.Google Scholar