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Infinite loop spaces
Author:
ISBN: 0691082073 0691082065 1400821258 Year: 1978 Volume: no. 90 Publisher: Princeton, N.J.

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Abstract

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.

Keywords

Algebraic topology --- Loop spaces --- Espaces de lacets --- Infinite loop spaces. --- Abelian group. --- Adams spectral sequence. --- Adjoint functors. --- Algebraic K-theory. --- Algebraic topology. --- Automorphism. --- Axiom. --- Bott periodicity theorem. --- CW complex. --- Calculation. --- Cartesian product. --- Cobordism. --- Coefficient. --- Cofibration. --- Cohomology operation. --- Cohomology ring. --- Cohomology. --- Commutative diagram. --- Continuous function. --- Counterexample. --- De Rham cohomology. --- Diagram (category theory). --- Differentiable manifold. --- Dimension. --- Discrete space. --- Disjoint union. --- Double coset. --- Eilenberg. --- Eilenberg–Steenrod axioms. --- Endomorphism. --- Epimorphism. --- Equivalence class. --- Euler class. --- Existential quantification. --- Explicit formulae (L-function). --- Exterior algebra. --- F-space. --- Fiber bundle. --- Fibration. --- Finite group. --- Function composition. --- Function space. --- Functor. --- Fundamental class. --- Fundamental group. --- Geometry. --- H-space. --- Homology (mathematics). --- Homomorphism. --- Homotopy category. --- Homotopy group. --- Homotopy. --- Hurewicz theorem. --- Inverse limit. --- J-homomorphism. --- K-theory. --- Limit (mathematics). --- Loop space. --- Mathematical induction. --- Maximal torus. --- Module (mathematics). --- Monoid. --- Monoidal category. --- Moore space. --- Morphism. --- Multiplication. --- Natural transformation. --- P-adic number. --- P-complete. --- Parameter space. --- Permutation. --- Prime number. --- Principal bundle. --- Principal ideal domain. --- Pullback (category theory). --- Quotient space (topology). --- Reduced homology. --- Riemannian manifold. --- Ring spectrum. --- Serre spectral sequence. --- Simplicial set. --- Simplicial space. --- Special case. --- Spectral sequence. --- Stable homotopy theory. --- Steenrod algebra. --- Subalgebra. --- Subring. --- Subset. --- Surjective function. --- Theorem. --- Theory. --- Topological K-theory. --- Topological ring. --- Topological space. --- Topology. --- Universal bundle. --- Universal coefficient theorem. --- Vector bundle. --- Weak equivalence (homotopy theory). --- Topologie algébrique


Book
Stable homotopy and generalised homology
Author:
ISBN: 0226005232 9780226005232 Year: 1974 Publisher: Chicago (Ill.) : University of Chicago press,


Book
Lectures on Lie groups
Author:
ISBN: 0805301178 080530116X 9780805301175 Year: 1969 Publisher: New York (N.Y.) : Benjamin,


Book
Infinite loop spaces
Author:
Year: 1978 Publisher: Princeton University Press, University of Tokyo Press

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Book
Algebraic topology : a student's guide
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Year: 1972 Publisher: Cambridge [Eng.] University Press

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Book
Infinite Loop Spaces (AM-90), Volume 90
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ISBN: 9781400821259 Year: 1978 Publisher: Princeton, NJ

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Infinite Loop Spaces (AM-90), Volume 90 : Hermann Weyl Lectures, The Institute for Advanced Study. (AM-90)
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ISBN: 9781400821259 9780691082066 Year: 1978 Publisher: Princeton, N.J. Princeton University Press

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Mathematics


Book
S.P. Novikov's work on operations on complex cobordism
Authors: ---
Year: 1967 Publisher: [Lieu de publication inconnu]: [éditeur inconnu],

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Topology --- Homology theory


Book
Stable homotopy theory : lectures delivered at the university of California at Berkeley 1961
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Year: 1966 Publisher: Berlin : Springer,

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Homotopy theory.


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Stable homotopy theory : lectures delivered at the university of California at Berkeley 1961
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Year: 1966 Publisher: Berlin: Springer,

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