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135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aSmoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 /$fMorris W. Hirsch, Barry Mazur
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1975
215   $a1 online resource (149 pages)
225 0 $aAnnals of Mathematics Studies ;$v269
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08145-X 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tPREFACE -- $tREFERENCES -- $tCONTENTS -- $tSMOOTHINGS OF PIECEWISE LINEAR MANIFOLDS I: PRODUCTS / $rHirsch, Morris W. -- $tSMOOTHINGS OF PIECEWISE LINEAR MANIFOLDS II: CLASSIFICATION / $rHirsch, Morris W. / Mazur, Barry -- $tBIBLIOGRAPHY -- $tBackmatter
330   $aThe intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology.Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology.The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
410  0$aAnnals of mathematics studies ;$vNumber 80.
606   $aPiecewise linear topology
606   $aManifolds (Mathematics)
610   $aAffine transformation.
610   $aApproximation.
610   $aAssociative property.
610   $aBijection.
610   $aBundle map.
610   $aClassification theorem.
610   $aCodimension.
610   $aCoefficient.
610   $aCohomology.
610   $aCommutative property.
610   $aComputation.
610   $aConvex cone.
610   $aConvolution.
610   $aCorollary.
610   $aCounterexample.
610   $aDiffeomorphism.
610   $aDifferentiable function.
610   $aDifferentiable manifold.
610   $aDifferential structure.
610   $aDimension.
610   $aDirect proof.
610   $aDivision by zero.
610   $aEmbedding.
610   $aEmpty set.
610   $aEquivalence class.
610   $aEquivalence relation.
610   $aEuclidean space.
610   $aExistential quantification.
610   $aExponential map (Lie theory).
610   $aFiber bundle.
610   $aFibration.
610   $aFunctor.
610   $aGrassmannian.
610   $aH-space.
610   $aHomeomorphism.
610   $aHomotopy.
610   $aIntegral curve.
610   $aInverse problem.
610   $aIsomorphism class.
610   $aK0.
610   $aLinearization.
610   $aManifold.
610   $aMathematical induction.
610   $aMilnor conjecture.
610   $aNatural transformation.
610   $aNeighbourhood (mathematics).
610   $aNormal bundle.
610   $aObstruction theory.
610   $aOpen set.
610   $aPartition of unity.
610   $aPiecewise linear.
610   $aPolyhedron.
610   $aReflexive relation.
610   $aRegular map (graph theory).
610   $aSheaf (mathematics).
610   $aSmoothing.
610   $aSmoothness.
610   $aSpecial case.
610   $aSubmanifold.
610   $aTangent bundle.
610   $aTangent vector.
610   $aTheorem.
610   $aTopological manifold.
610   $aTopological space.
610   $aTopology.
610   $aTransition function.
610   $aTransitive relation.
610   $aVector bundle.
610   $aVector field.
615  0$aPiecewise linear topology.
615  0$aManifolds (Mathematics)
676   $a514/.224
700   $aHirsch$b Morris W., $013761
702   $aMazur$b Barry, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154743503321
996   $aSmoothings of Piecewise Linear Manifolds. (AM-80), Volume 80$92839521
997   $aUNINA