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035   $a(DE-B1597)9781400881475
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100   $a20190708d2016      fg 
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aClassifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92 /$fR. James Milgram, Ib Madsen
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1980
215   $a1 online resource (296 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v229
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08225-1 
311   $a0-691-08226-X 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tCONTENTS -- $tINTRODUCTION -- $tCHAPTER 1. CLASSIFYING SPACES AND COBORDISM -- $tCHAPTER 2. THE SURGERY CLASSIFICATION OF MANIFOLDS -- $tCHAPTER 3. THE SPACES SG AND BSG -- $tCHAPTER 4. THE HOMOTOPY STRUCTURE OF G/PL AND G/TOP -- $tCHAPTER 5. THE HOMOTOPY STRUCTURE OF MSPL[½] AND MSTOP[½] -- $tCHAPTER 6 . INFINITE LOOP SPACES AND THEIR HOMOLOGY OPERATIONS -- $tCHAPTER 7. THE 2-LOCAL STRUCTURE OF B(G/TOP) -- $tCHAPTER 8 . THE TORSION FREE STRUCTURE OF THE ORIENTED COBORDISM RINGS -- $tCHAPTER 9. THE TORSION FREE COHOMOLOGY OF G/TOP AND G/PL -- $tCHAPTER 10. THE TORSION FREE COHOMOLOGY OF BTOP AND BPL -- $tCHAPTER 11. INTEGRALITY THEOREMS -- $tCHAPTER 12. THE SMOOTH SURGERY CLASSES AND H*(BTOP; ?/2) -- $tCHAPTER 13. THE BOCKSTEIN SPECTRAL SEQUENCE FOR BTOP -- $tCHAPTER 14. THE TYPES OF TORSION GENERATORS -- $tAPPENDIX. THE PROOFS OF 13.12, 13.13, AND 13.15 -- $tBIBLIOGRAPHY -- $tINDEX -- $tBackmatter
330   $aBeginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.
410  0$aAnnals of mathematics studies ;$vNumber 92.
606   $aManifolds (Mathematics)
606   $aClassifying spaces
606   $aSurgery (Topology)
606   $aCobordism theory
610   $aBijection.
610   $aCalculation.
610   $aCharacteristic class.
610   $aClassification theorem.
610   $aClassifying space.
610   $aClosed manifold.
610   $aCobordism.
610   $aCoefficient.
610   $aCohomology.
610   $aCommutative diagram.
610   $aCommutative property.
610   $aComplex projective space.
610   $aConnected sum.
610   $aCorollary.
610   $aCup product.
610   $aDiagram (category theory).
610   $aDifferentiable manifold.
610   $aDisjoint union.
610   $aDisk (mathematics).
610   $aEffective method.
610   $aEilenberg?Moore spectral sequence.
610   $aElaboration.
610   $aEquivalence class.
610   $aExact sequence.
610   $aExterior algebra.
610   $aFiber bundle.
610   $aFibration.
610   $aFunction composition.
610   $aH-space.
610   $aHomeomorphism.
610   $aHomomorphism.
610   $aHomotopy fiber.
610   $aHomotopy group.
610   $aHomotopy.
610   $aHopf algebra.
610   $aIterative method.
610   $aLoop space.
610   $aManifold.
610   $aMassey product.
610   $aN-sphere.
610   $aNormal bundle.
610   $aObstruction theory.
610   $aPairing.
610   $aPermutation.
610   $aPiecewise linear manifold.
610   $aPiecewise linear.
610   $aPolynomial.
610   $aPrime number.
610   $aProjective space.
610   $aSequence.
610   $aSimply connected space.
610   $aSpecial case.
610   $aSpin structure.
610   $aSteenrod algebra.
610   $aSubset.
610   $aSummation.
610   $aTensor product.
610   $aTheorem.
610   $aTopological group.
610   $aTopological manifold.
610   $aTopology.
610   $aTotal order.
615  0$aManifolds (Mathematics)
615  0$aClassifying spaces.
615  0$aSurgery (Topology)
615  0$aCobordism theory.
676   $a514/.223
700   $aMadsen$b Ib, $055804
702   $aMilgram$b R. James, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154749003321
996   $aClassifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92$92788679
997   $aUNINA