LEADER 04735nam 2200721 a 450 001 9910456689603321 005 20200520144314.0 010 $a1-282-45837-X 010 $a9786612458378 010 $a1-4008-2906-2 024 7 $a10.1515/9781400829064 035 $a(CKB)2550000000003519 035 $a(EBL)483509 035 $a(OCoLC)593214464 035 $a(SSID)ssj0000338850 035 $a(PQKBManifestationID)11230411 035 $a(PQKBTitleCode)TC0000338850 035 $a(PQKBWorkID)10298053 035 $a(PQKB)11597985 035 $a(MiAaPQ)EBC483509 035 $a(DE-B1597)447046 035 $a(OCoLC)979970184 035 $a(DE-B1597)9781400829064 035 $a(Au-PeEL)EBL483509 035 $a(CaPaEBR)ebr10359240 035 $a(CaONFJC)MIL245837 035 $a(EXLCZ)992550000000003519 100 $a20080229d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe hypoelliptic Laplacian and Ray-Singer metrics$b[electronic resource] /$fJean-Michel Bismut, Gilles Lebeau 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2008 215 $a1 online resource (378 p.) 225 1 $aAnnals of mathematics studies ;$vno. 167 300 $aDescription based upon print version of record. 311 $a0-691-13731-5 311 $a0-691-13732-3 320 $aIncludes bibliographical references (p. [353]-357) and indexes. 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tChapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles -- $tChapter 2. The hypoelliptic Laplacian on the cotangent bundle -- $tChapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel -- $tChapter 4. Hypoelliptic Laplacians and odd Chern forms -- $tChapter 5. The limit as t ? +? and b ? 0 of the superconnection forms -- $tChapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics -- $tChapter 7. The hypoelliptic torsion forms of a vector bundle -- $tChapter 8. Hypoelliptic and elliptic torsions: a comparison formula -- $tChapter 9. A comparison formula for the Ray-Singer metrics -- $tChapter 10. The harmonic forms for b ? 0 and the formal Hodge theorem -- $tChapter 11. A proof of equation (8.4.6) -- $tChapter 12. A proof of equation (8.4.8) -- $tChapter 13. A proof of equation (8.4.7) -- $tChapter 14. The integration by parts formula -- $tChapter 15. The hypoelliptic estimates -- $tChapter 16. Harmonic oscillator and the J0 function -- $tChapter 17. The limit of A'2?b,±H as b ? 0 -- $tBibliography -- $tSubject Index -- $tIndex of Notation 330 $aThis book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion. The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained. The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions. 410 0$aAnnals of mathematics studies ;$vno. 167. 606 $aDifferential equations, Hypoelliptic 606 $aLaplacian operator 606 $aMetric spaces 608 $aElectronic books. 615 0$aDifferential equations, Hypoelliptic. 615 0$aLaplacian operator. 615 0$aMetric spaces. 676 $a515/.7242 686 $aSK 620$2rvk 700 $aBismut$b Jean-Michel$044924 701 $aLebeau$b Gilles$063020 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910456689603321 996 $aHypoelliptic laplacian and ray-singer metrics$91013782 997 $aUNINA LEADER 04819nam 2200829 450 001 9910780563003321 005 20230912140704.0 010 $a1-282-03690-4 010 $a9786612036903 010 $a1-4426-7930-1 024 7 $a10.3138/9781442679306 035 $a(CKB)2420000000004325 035 $a(EBL)3255360 035 $a(OCoLC)244768017 035 $a(SSID)ssj0000308302 035 $a(PQKBManifestationID)11260628 035 $a(PQKBTitleCode)TC0000308302 035 $a(PQKBWorkID)10259329 035 $a(PQKB)11604784 035 $a(CaBNvSL)thg00600579 035 $a(DE-B1597)479193 035 $a(OCoLC)987938833 035 $a(DE-B1597)9781442679306 035 $a(Au-PeEL)EBL4671906 035 $a(CaPaEBR)ebr11257595 035 $a(OCoLC)1100666999 035 $a(MdBmJHUP)musev2_105173 035 $a(VaAlCD)20.500.12592/xx2f4g 035 $a(schport)gibson_crkn/2009-12-01/6/418074 035 $a(MiAaPQ)EBC4671906 035 $a(MiAaPQ)EBC3255360 035 $a(EXLCZ)992420000000004325 100 $a20160922h20002000 uy 0 101 0 $aeng 135 $aurun#---auuuu 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aRethinking church, state, and modernity $eCanada between Europe and America /$fedited by David Lyon and Marguerite Van Die 210 1$aToronto, [Ontario] ;$aBuffalo, [New York] ;$aLondon, [England] :$cUniversity of Toronto Press,$d2000. 210 4$d©2000 215 $a1 online resource (xiv, 353 pages) 300 $aDescription based upon print version of record. 311 0 $a0-8020-8213-0 311 0 $a0-8020-4408-5 320 $aIncludes bibliographical references and index. 327 $gPart One:$tPatterns and flows --$tCanada in comparative perspective /$rDavid Martin --$tCanadian religion: heritage and project /$rRoger O'Toole --$tIndividualism religious and modern: communities and discontinuities /$rDaniele Hervieu-Leger --$gPart Two:$tAlignments and alliances --$tChurch and state in institutional flux: Canada and the United States /$rKevin J. Christiano --$tTrudeau, God, and the Canadian constitution: religion, human rights, and government authority in the making of the 1982 constitution /$rGeorge Egerton --$tBearing witness: Christian groups engage Canadian politics since the 1960s /$rJohn G. Stackhouse --$gPart Three:$tCivic and civil religion --$tResisting the 'No Man's Land' of private religion: the Catholic Church and public politics in Quebec /$rDavid Seljak --$tCatholicism and secularization in Quebec /$rGregory Baum --$tCivil religion and the problem of national unity: the 1995 Quebec Referendum Crisis /$rHarry H. Hiller --$gPart Four:$tBelieving and belonging --$tModern forms of the religious life: denomination, church, and invisible religion in Canada, the United States, and Europe /$rPeter Beyer --$t'For by him all things were created ... visible and invisible': sketching the contours of public and private religion in North America /$rAndrew S. Greenville --$tGeneric evangelicalism? Comparing evangelical subcultures in Canada and the United States /$rSam Reimer --$gPart Five:$tidentity, gender, body --$tSteeple or the shelter? Family violence and church-and-state relations in contemporary Canada /$rNancy Nason-Clark --$tPolitics of the body in Canada and the United States /$rJohn H. Simpson --$tConsumers and citizens: religion, identity, and politics in Canadian and the United States /$rWilliam H. Katerberg. 330 1 $a"Rethinking Church, State, and Modernity considers some central concepts in the sociology and history of religion and explores how Canada's religious experience is distinctive in the modern world. The contributors to this volume challenge the institutional approach that stresses a strict division between 'church' and 'state, ' which seems increasingly inappropriate in late-modern and post-modern society and instead, favour a more fluid interpretation."--Jacket. 606 $aChurch and state$zCanada 606 $aChurch and state$zUnited States 606 $aReligion and state$zCanada 606 $aReligion and state$zUnited States 607 $aCanada$xChurch history 607 $aCanada$xReligion 608 $aLivres numeriques. 608 $aChurch history. 608 $ae-books. 608 $aElectronic books. 615 0$aChurch and state 615 0$aChurch and state 615 0$aReligion and state 615 0$aReligion and state 676 $a322/.1/0971 702 $aLyon$b David A., 702 $aVan Die$b Marguerite, 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780563003321 996 $aRethinking church, state, and modernity$93787597 997 $aUNINA