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dc.contributor.authorBohlen, Karsten
dc.contributor.authorSchrohe, Elmar
dc.date.accessioned2016-10-25T12:33:36Z
dc.date.available2016-10-25T12:33:36Z
dc.date.issued2016-10
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1256
dc.descriptionOWLF 2015en_US
dc.description.abstractWe prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). After introducing a renormalized supertrace on Lie manifolds with spin structure, defined on a suitable class of rapidly decaying functions, the proof of the index theorem relies on a rescaling technique similar in spirit to Getzler's rescaling. With a given Lie manifold we associate an appropriate integrating Lie groupoid. We then describe the heat kernel of a geometric Dirac operator via a functional calculus with values in the convolution algebra of sections of the rescaled bundle over the adiabatic groupoid and introduce a rescaling of the heat kernel encoded in a vector bundle over the adiabatic groupoid. Finally, we calculate the right coefficient in the heat kernel expansion using the Lichnerowicz theorem on the fibers of the groupoid and the Lie manifold.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2016,18
dc.subjectLie manifolden_US
dc.subjectIndex theoryen_US
dc.subjectGroupoiden_US
dc.titleGetzler rescaling via adiabatic deformation and a renormalized local index formulaen_US
dc.typePreprinten_US
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.de
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.en
dc.identifier.doi10.14760/OWP-2016-18
local.scientificprogramOWLF 2015en_US
local.series.idOWP-2016-18
local.subject.msc58
local.subject.msc53
dc.identifier.urnurn:nbn:de:101:1-20161010279
dc.identifier.ppn1658987896


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