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. |
Contents
CHAPTER 1 | 3 |
CHAPTER 2 | 30 |
category namely the category | 68 |
CHAPTER 3 | 74 |
7₁X | 85 |
CHAPTER 4 | 96 |
CHAPTER 5 | 132 |
CHAPTER 6 | 142 |
that ensures | 189 |
CHAPTER 7 | 192 |
REFERENCES | 197 |
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Infinite Loop Spaces (AM-90), Volume 90: Hermann Weyl Lectures, The ... John Frank Adams Limited preview - 1978 |
Common terms and phrases
Adams conjecture algebraic argument axioms base-point Boardman and Vogt bundle Chapter classifying space cohomology theory composite consider construction Corollary corresponding CW-complex define E-space Eilenberg-MacLane space element equivalent example fibering fibre finite complex following diagram formula functor geometry H-space higher homotopies homology homomorphism homotopy classes homotopy groups homotopy-theory induced map infinite loop map infinite loop spaces isomorphism J-homomorphism K₁ little n-cubes localization loop-space map f map of spectra module monoid morphisms n-sheeted covering N-spectrum natural transformation object operad oth term p-adic p-adic topology Pa,b permutations Priddy prime problem product map properties Proposition proves Lemma Quillen real K-theory 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 theorem tion topologists universal coefficient theorem vector-bundles zero
Popular passages
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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.