LEADER 04344nam 2200709Ia 450 001 9910813326203321 005 20200520144314.0 010 $a1-280-49429-8 010 $a9786613589521 010 $a1-4008-4272-7 024 7 $a10.1515/9781400842728 035 $a(CKB)2550000001273118 035 $a(EBL)870005 035 $a(OCoLC)780425982 035 $a(SSID)ssj0000623887 035 $a(PQKBManifestationID)11388715 035 $a(PQKBTitleCode)TC0000623887 035 $a(PQKBWorkID)10656329 035 $a(PQKB)11538876 035 $a(StDuBDS)EDZ0000406948 035 $a(DE-B1597)447835 035 $a(OCoLC)979624183 035 $a(DE-B1597)9781400842728 035 $a(Au-PeEL)EBL870005 035 $a(CaPaEBR)ebr10539569 035 $a(CaONFJC)MIL358952 035 $z(PPN)199244308 035 $a(PPN)18795965X 035 $a(FR-PaCSA)88837999 035 $a(MiAaPQ)EBC870005 035 $a(EXLCZ)992550000001273118 100 $a20111018d2012 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 14$aThe decomposition of global conformal invariants /$fSpyros Alexakis 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2012 215 $a1 online resource (460 p.) 225 1 $aAnnals of mathematics studies ;$vno. 182 300 $aDescription based upon print version of record. 311 $a0-691-15348-5 311 $a0-691-15347-7 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tAcknowledgments --$t1. Introduction --$t2. An Iterative Decomposition of Global Conformal Invariants: The First Step --$t3. The Second Step: The Fefferman-Graham Ambient Metric and the Nature of the Decomposition --$t4. A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition --$t5. The Inductive Step of the Fundamental Proposition: The Simpler Cases --$t6. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part I --$t7. The Inductive Step of the Fundamental Proposition: The Hard Cases, Part II --$tA. Appendix --$tBibliography --$tIndex of Authors and Terms --$tIndex of Symbols 330 $aThis book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser and Schwimmer asserted that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern-Gauss-Bonnet integrand. This book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants--such as the classical Riemannian invariants and the more recently studied conformal invariants--and the study of global invariants, in this case conformally invariant integrals. Key tools used to establish this connection include the Fefferman-Graham ambient metric and the author's super divergence formula. 410 0$aAnnals of mathematics studies ;$vno. 182. 606 $aConformal invariants 606 $aDecomposition (Mathematics) 615 0$aConformal invariants. 615 0$aDecomposition (Mathematics) 676 $a518 700 $aAlexakis$b Spyros$f1978-$01629867 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813326203321 996 $aThe decomposition of global conformal invariants$93967866 997 $aUNINA