Infinite Loop Spaces

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Princeton University Press, 1978 - Mathematics - 214 pages
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The theory of infinite loop spaces has been the center of much recent activity in algebraic topology. Frank Adams surveys this extensive work for researchers and students. Among the major topics covered are generalized cohomology theories and spectra; infinite-loop space machines in the sense of Boadman-Vogt, May, and Segal; localization and group completion; the transfer; the Adams conjecture and several proofs of it; and the recent theories of Adams and Priddy and of Madsen, Snaith, and Tornehave.

  

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Contents

BACKGROUND AND PRELIMINARIES
3
MACHINERY
30
LOCALIZATION AND GROUP COMPLETION
74
TRANSFER
96
THE ADAMS CONJECTURE
132
THE SPECIAL CASE OF KTHEORY SPECTRA
142
THE STATE OF THE
192
INDEX
211
Copyright

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Page 198 - MF Atiyah and R. Bott, On the periodicity theorem for complex vector bundles, Acta Math.
Page 200 - REFERENCES 1. R. Bott, The stable homotopy of the classical groups, Proc. Nat. Acad. Sci. USA vol. 43 (1951) pp.
Page 206 - G. Nishida, Cohomology operations in iterated loop spaces, Proc. Japan Acad. 44 (1968), 104-109.
Page 198 - Topology 5 (1966), 21-71. 2. JF Adams and G. Walker, On Complex Stiefel manifolds, Proc. Cambridge Philos. Soc. 61 (I960), 81-103.
Page 200 - A. Borei and F. Hirzebruch, Characteristic classes and homogeneous spaces I, Amer. J. Math.
Page 201 - EH Brown, Jr., Cohomology theories, Ann. of Math. (2) 75 (1962), 467-484; correction, ibid.

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