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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.

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

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This collection brings together influential papers by mathematicians exploring the research frontiers of topology, one of the most important developments of modern mathematics. The papers cover a wide range of topological specialties, including tools for the analysis of group actions on manifolds, calculations of algebraic K-theory, a result on analytic structures on Lie group actions, a presentation of the significance of Dirac operators in smoothing theory, a discussion of the stable topology of 4-manifolds, an answer to the famous question about symmetries of simply connected manifolds, and a fresh perspective on the topological classification of linear transformations. The contributors include A. Adem, A. H. Assadi, M. Bökstedt, S. E. Cappell, R. Charney, M. W. Davis, P. J. Eccles, M. H. Freedman, I. Hambleton, J. C. Hausmann, S. Illman, G. Katz, M. Kreck, W. Lück, I. Madsen, R. J. Milgram, J. Morava, E. K. Pedersen, V. Puppe, F. Quinn, A. Ranicki, J. L. Shaneson, D. Sullivan, P. Teichner, Z. Wang, and S. Weinberger.

Topology --- Adjunction (field theory). --- Algebraic cycle. --- Algebraic topology. --- Analytic function. --- Automorphism. --- Base change. --- Basis (linear algebra). --- Borel conjecture. --- Characteristic class. --- Circle group. --- Classifying space. --- Cobordism. --- Codimension. --- Cohomology ring. --- Cohomology. --- Combinatorial group theory. --- Commutative diagram. --- Commutative property. --- Compactification (mathematics). --- Coxeter group. --- Cyclic group. --- Cyclic homology. --- Diagram (category theory). --- Diffeomorphism. --- Differentiable manifold. --- Differential topology. --- Dimension (vector space). --- Dirac operator. --- Discrete valuation ring. --- Divisor (algebraic geometry). --- Elliptic operator. --- Equivariant K-theory. --- Equivariant cohomology. --- Equivariant map. --- Exterior (topology). --- Exterior algebra. --- Fiber bundle. --- Fibration. --- Fundamental group. --- Gauss map. --- Geometrization conjecture. --- Group algebra. --- H-cobordism. --- Homeomorphism. --- Homotopy fiber. --- Homotopy group. --- Homotopy. --- Hopf algebra. --- Identity matrix. --- Inclusion map. --- Intersection form (4-manifold). --- Isomorphism class. --- J-homomorphism. --- Knot theory. --- L-theory. --- Lens space. --- Lie algebra. --- Lie group. --- Linear algebra. --- Mapping cone (homological algebra). --- Mapping cone (topology). --- Marriage theorem. --- Metric space. --- Moduli space. --- Motivic cohomology. --- Neighbourhood (mathematics). --- Operator norm. --- Pushout (category theory). --- Quasi-isometry. --- Quotient space (topology). --- Real projective space. --- Regularization (mathematics). --- Representation theory. --- Riemann surface. --- Riemannian manifold. --- Set (mathematics). --- Sheaf (mathematics). --- Sign (mathematics). --- Simplicial complex. --- Stable homotopy theory. --- Subgroup. --- Submanifold. --- Submersion (mathematics). --- Subset. --- Support (mathematics). --- Sylow theorems. --- Tangent space. --- Theorem. --- Topological K-theory. --- Topological group. --- Topological manifold. --- Topological space. --- Topology. --- Torsion sheaf. --- Transversality (mathematics). --- Unification (computer science). --- Vector bundle. --- Whitehead torsion. --- Zariski topology. --- Zorn's lemma.