LEADER 05383nam 22013935 450 001 9910154743503321 005 20190708092533.0 010 $a1-4008-8168-4 024 7 $a10.1515/9781400881680 035 $a(CKB)3710000000631382 035 $a(SSID)ssj0001651330 035 $a(PQKBManifestationID)16426278 035 $a(PQKBTitleCode)TC0001651330 035 $a(PQKBWorkID)12661656 035 $a(PQKB)11031146 035 $a(MiAaPQ)EBC4738551 035 $a(DE-B1597)467914 035 $a(OCoLC)979633757 035 $a(DE-B1597)9781400881680 035 $a(EXLCZ)993710000000631382 100 $a20190708d2016 fg 101 0 $aeng 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 LEADER 02952oam 22005414a 450 001 9910697857703321 005 20081209090419.0 035 $a(CKB)5470000002392405 035 $a(OCoLC)84667315 035 $a(EXLCZ)995470000002392405 100 $a20060920d1993 ua 0 101 0 $aeng 135 $aurcn||||a|||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe journey of Native American people with serious mental illness$b[electronic resource] $eexecutive summary /$f[written by James H. Zahniser, A. Marie Sanchez, and Frank D. McGuirk] 210 1$a[Washington, DC] :$cSAMHSA's National Mental Health Information Center, Center for Mental Health,$d[1993?] 215 $a1 electronic text $cHTML file 300 $aTitle from title screen caption (viewed Oct. 11, 2006). 330 3 $aSeveral leaders from the National Institute of Mental Health (NIMH), the Center for Mental Health Services (CMHS), the Mental Health Program of the Indian Health Service and the National Association of State Mental Health Program Directors (NASMHPD) joined with others in organizing the first national conference on Native American people with serious mental illness, in order to bring together State, tribal and IHS mental health officials, providers, families, and consumers, to discuss the challenges that face Federal agencies and the Indian nations. The goal of the conference was to create mechanisms to implement the shared vision of an effective, comprehensive service delivery system for Native Americans with serious and persistent mental illness. 517 $aJourney of Native American people with serious mental illness 606 $aIndians of North America$xMental health services$vCongresses 606 $aMental Health Services$xorganization & administration 606 $aIndians, North American 606 $aMental Disorders$xethnology 607 $aUnited States 608 $aCongress. 608 $aConference papers and proceedings.$2lcgft 615 0$aIndians of North America$xMental health services 615 12$aMental Health Services$xorganization & administration. 615 22$aIndians, North American. 615 22$aMental Disorders$xethnology. 700 $aZahniser$b James H$01399521 701 $aSanchez$b Marie$01399522 701 $aMcGuirk$b Frank D$01399523 712 02$aUnited States.$bIndian Health Service.$bMental Health Programs Branch. 712 02$aNational Mental Health Information Center (U.S.) 712 02$aNational Institute of Mental Health (U.S.) 712 02$aCenter for Mental Health Services (U.S.) 712 02$aNational Association of State Mental Health Program Directors. 801 0$bDNLM 801 1$bNLM 801 2$bGPO 906 $aBOOK 912 $a9910697857703321 996 $aThe journey of Native American people with serious mental illness$93464814 997 $aUNINA