Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T01:08:16.406Z Has data issue: false hasContentIssue false

Generalized splitting theorems

Published online by Cambridge University Press:  24 October 2008

J. P. May
Affiliation:
University of Chicago
L. R. Taylor
Affiliation:
University of Chicago

Extract

In (5), we and Fred Cohen gave some quite general splitting theorems. These described how to decompose the suspension spectra of certain filtered spaces CX as wedges of the suspension spectra of their successive filtration quotients Dq X. The spaces CX were of the form Cr × Xr/(˜) for suitable sequences of spaces {Cr} and {Xr}, and the construction CX was intended to be a reworking in ‘proper generality’ of the constructions introduced in (9).

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1983

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)Boardman, J. M. and Vogt, R. M.Homotopy invariant structures on topological spaces. Springer Lecture Notes in Mathematics no. 347 (1973).CrossRefGoogle Scholar
(2)Caruso, J., Cohen, F. R., May, J. P. and Taylor, L. R.James maps, Segal maps, and the Kahn-Priddy theorem. Amer. J. Math. (to appear.)Google Scholar
(3)Caruso, J. and May, J. P. The equivariant splitting and Kahn-Priddy theorems. (To appear.)Google Scholar
(4)Cohen, F. R. The unstable decomposition of Ω2Ω2X and its applications. (Preprint.)Google Scholar
(5)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of certain spaces CX. Math. Proc. Cambridge Phil. Soc. 84 (1978), 465496.CrossRefGoogle Scholar
(6)Cohen, F. R., May, J. P. and Taylor, L. R.Splitting of some more spaces. Math. Proc. Cambridge Phil. Soc. 86 (1979), 227236.CrossRefGoogle Scholar
(7)Gray, B.On the homotopy groups of mapping cones. Proc. Adv. Study Inst. Alg. Top (Aarhus, Denmark, 1970), pp. 104142.Google Scholar
(8)MacLane, S.Categories for the working mathematician (Springer-Verlag, 1971).Google Scholar
(9)May, J. P.The geometry of iterated loop spaces. Springer Lecture Notes in Mathematics, no. 271 (1972).CrossRefGoogle Scholar
(10)May, J. P. and Thomason, R.The uniqueness of infinite loop space machines. Topology 17 (1978), 205224.CrossRefGoogle Scholar