## Infinite Loop SpacesThe 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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2-primary Adams conjecture algebraic argument axioms base-point Becker and Gottlieb Boardman and Vogt bundle Chapter classifying space coefficient groups cohomology theory composite consider construction Corollary corresponding CW-complex define E^-space Eilenberg-MacLane space element example fibering fibre finite complex following diagram formula geometry give H-space higher homotopies homology homomorphism homotopy classes homotopy groups homotopy-theory induced map infinite loop map infinite loop spaces integers isomorphism J-homomorphism little n-cubes localization loop-space map f map of spectra mod pn module monoid morphisms n-sheeted covering natural transformation object operad p-adic p-adic topology permutations PRETHEOREM Priddy prime problem product map PROP properties Proposition proves Lemma Q-spectrum Quillen real K-theory replace result sense Serre similarly simplicial set simplicial space Snaith and Tornehave spectral sequence spectrum stable homotopy theory Stasheff structure maps subgroup sufficient suitable suppose given tion topologists torsion-free universal coefficient theorem vector-bundles zero

### Popular passages

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Page 200 - REFERENCES 1. R. Bott, The stable homotopy of the classical groups, Proc. Nat. Acad. Sci. USA vol. 43 (1951) pp.

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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.