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101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aC*-Algebra Extensions and K-Homology. (AM-95), Volume 95 /$fRonald G. Douglas
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1980
215   $a1 online resource (94 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v228
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08265-0 
311   $a0-691-08266-9 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tContents -- $tPreface -- $tChapter 1. An Overview -- $tChapter 2. Ext as a Group -- $tChapter 3. Ext as a Homotopy Functor -- $tChapter 4. Generalized Homology Theory and Periodicity -- $tChapter 5. Ext as K-Homology -- $tChapter 6. Index Theorems snd Novikov's Higher Signatures -- $tReferences -- $tIndex -- $tIndex of Symbols -- $tBackmatter
330   $aRecent developments in diverse areas of mathematics suggest the study of a certain class of extensions of C*-algebras. Here, Ronald Douglas uses methods from homological algebra to study this collection of extensions. He first shows that equivalence classes of the extensions of the compact metrizable space X form an abelian group Ext (X). Second, he shows that the correspondence X ? Ext (X) defines a homotopy invariant covariant functor which can then be used to define a generalized homology theory. Establishing the periodicity of order two, the author shows, following Atiyah, that a concrete realization of K-homology is obtained.
410  0$aAnnals of mathematics studies ;$vNumber 95.
606   $aC*-algebras
606   $aK-theory
606   $aAlgebra, Homological
610   $aAddition.
610   $aAffine transformation.
610   $aAlgebraic topology.
610   $aAtiyah?Singer index theorem.
610   $aAutomorphism.
610   $aBanach algebra.
610   $aBijection.
610   $aBoundary value problem.
610   $aBundle map.
610   $aC*-algebra.
610   $aCalculation.
610   $aCardinal number.
610   $aCategory of abelian groups.
610   $aCharacteristic class.
610   $aChern class.
610   $aClifford algebra.
610   $aCoefficient.
610   $aCohomology.
610   $aCompact operator.
610   $aCompletely positive map.
610   $aContact geometry.
610   $aContinuous function.
610   $aCorollary.
610   $aDiagram (category theory).
610   $aDiffeomorphism.
610   $aDifferentiable manifold.
610   $aDifferential operator.
610   $aDimension (vector space).
610   $aDimension function.
610   $aDimension.
610   $aDirect integral.
610   $aDirect proof.
610   $aEigenvalues and eigenvectors.
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aEssential spectrum.
610   $aEuler class.
610   $aExact sequence.
610   $aExistential quantification.
610   $aFiber bundle.
610   $aFinite group.
610   $aFredholm operator.
610   $aFredholm.
610   $aFree abelian group.
610   $aFundamental class.
610   $aFundamental group.
610   $aHardy space.
610   $aHermann Weyl.
610   $aHilbert space.
610   $aHomological algebra.
610   $aHomology (mathematics).
610   $aHomomorphism.
610   $aHomotopy.
610   $aIdeal (ring theory).
610   $aInner automorphism.
610   $aIrreducible representation.
610   $aK-group.
610   $aK-theory.
610   $aLebesgue space.
610   $aLocally compact group.
610   $aMaximal compact subgroup.
610   $aMichael Atiyah.
610   $aMonomorphism.
610   $aMorphism.
610   $aNatural number.
610   $aNatural transformation.
610   $aNormal operator.
610   $aOperator algebra.
610   $aOperator norm.
610   $aOperator theory.
610   $aOrthogonal group.
610   $aPairing.
610   $aPiecewise linear manifold.
610   $aPolynomial.
610   $aPontryagin class.
610   $aPositive and negative parts.
610   $aPositive map.
610   $aPseudo-differential operator.
610   $aQuaternion.
610   $aQuotient algebra.
610   $aSelf-adjoint operator.
610   $aSelf-adjoint.
610   $aSimply connected space.
610   $aSmooth structure.
610   $aSpecial case.
610   $aStein manifold.
610   $aStrong topology.
610   $aSubalgebra.
610   $aSubgroup.
610   $aSubset.
610   $aSummation.
610   $aTangent bundle.
610   $aTheorem.
610   $aTodd class.
610   $aTopology.
610   $aTorsion subgroup.
610   $aUnitary operator.
610   $aUniversal coefficient theorem.
610   $aVariable (mathematics).
610   $aVon Neumann algebra.
615  0$aC*-algebras.
615  0$aK-theory.
615  0$aAlgebra, Homological.
676   $a512/.55
700   $aDouglas$b Ronald G., $054969
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154752903321
996   $a-Algebra Extensions and K-Homology. (AM-95), Volume 95$92988187
997   $aUNINA