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181   $ctxt
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200 10$aNilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128 /$fDouglas C. Ravenel
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1993
215   $a1 online resource (225 pages)
225 0 $aAnnals of Mathematics Studies ;$v310
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-02572-X 
311   $a0-691-08792-X 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tContents -- $tPreface -- $tIntroduction -- $tChapter 1. The main theorems -- $tChapter 2. Homotopy groups and the chromatic filtration -- $tChapter 3. MU-theory and formal group laws -- $tChapter 4. Morava's orbit picture and Morava stabilizer groups -- $tChapter 5. The thick subcategory theorem -- $tChapter 6. The periodicity theorem -- $tChapter 7. Bousfield localization and equivalence -- $tChapter 8. The proofs of the localization, smash product and chromatic convergence theorems -- $tChapter 9. The proof of the nilpotence theorem -- $tAppendix A. Some tools from homotopy theory -- $tAppendix B. Complex bordism and BP-theory -- $tAppendix C. Some idempotents associated with the symmetric group -- $tBibliography -- $tIndex
330   $aNilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
410  0$aAnnals of mathematics studies ;$vno. 128.
606   $aHomotopy theory
610   $aAbelian category.
610   $aAbelian group.
610   $aAdams spectral sequence.
610   $aAdditive category.
610   $aAffine space.
610   $aAlgebra homomorphism.
610   $aAlgebraic closure.
610   $aAlgebraic structure.
610   $aAlgebraic topology (object).
610   $aAlgebraic topology.
610   $aAlgebraic variety.
610   $aAlgebraically closed field.
610   $aAtiyah?Hirzebruch spectral sequence.
610   $aAutomorphism.
610   $aBoolean algebra (structure).
610   $aCW complex.
610   $aCanonical map.
610   $aCantor set.
610   $aCategory of topological spaces.
610   $aCategory theory.
610   $aClassification theorem.
610   $aClassifying space.
610   $aCohomology operation.
610   $aCohomology.
610   $aCokernel.
610   $aCommutative algebra.
610   $aCommutative ring.
610   $aComplex projective space.
610   $aComplex vector bundle.
610   $aComputation.
610   $aConjecture.
610   $aConjugacy class.
610   $aContinuous function.
610   $aContractible space.
610   $aCoproduct.
610   $aDifferentiable manifold.
610   $aDisjoint union.
610   $aDivision algebra.
610   $aEquation.
610   $aExplicit formulae (L-function).
610   $aFunctor.
610   $aG-module.
610   $aGroupoid.
610   $aHomology (mathematics).
610   $aHomomorphism.
610   $aHomotopy category.
610   $aHomotopy group.
610   $aHomotopy.
610   $aHopf algebra.
610   $aHurewicz theorem.
610   $aInclusion map.
610   $aInfinite product.
610   $aInteger.
610   $aInverse limit.
610   $aIrreducible representation.
610   $aIsomorphism class.
610   $aK-theory.
610   $aLoop space.
610   $aMapping cone (homological algebra).
610   $aMathematical induction.
610   $aModular representation theory.
610   $aModule (mathematics).
610   $aMonomorphism.
610   $aMoore space.
610   $aMorava K-theory.
610   $aMorphism.
610   $aN-sphere.
610   $aNoetherian ring.
610   $aNoetherian.
610   $aNoncommutative ring.
610   $aNumber theory.
610   $aP-adic number.
610   $aPiecewise linear manifold.
610   $aPolynomial ring.
610   $aPolynomial.
610   $aPower series.
610   $aPrime number.
610   $aPrincipal ideal domain.
610   $aProfinite group.
610   $aReduced homology.
610   $aRing (mathematics).
610   $aRing homomorphism.
610   $aRing spectrum.
610   $aSimplicial complex.
610   $aSimply connected space.
610   $aSmash product.
610   $aSpecial case.
610   $aSpectral sequence.
610   $aSteenrod algebra.
610   $aSub"ient.
610   $aSubalgebra.
610   $aSubcategory.
610   $aSubring.
610   $aSymmetric group.
610   $aTensor product.
610   $aTheorem.
610   $aTopological space.
610   $aTopology.
610   $aVector bundle.
610   $aZariski topology.
615  0$aHomotopy theory.
676   $a514/.24
700   $aRavenel$b Douglas C., $057251
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154751603321
996   $aNilpotence and Periodicity in Stable Homotopy Theory. (AM-128), Volume 128$92788034
997   $aUNINA