Infinitesimal symmetries of Dixmier-Douady gerbes

dc.contributor.advisorFreed, Daniel S.en
dc.contributor.committeeMemberAllcock, Danielen
dc.contributor.committeeMemberBen-Zvi, Daviden
dc.contributor.committeeMemberKeel, Seanen
dc.contributor.committeeMemberMeinrenken, Eckharden
dc.creatorCollier, Braxton Livingstonen
dc.date.accessioned2012-11-20T15:05:19Zen
dc.date.available2012-11-20T15:05:19Zen
dc.date.issued2012-08en
dc.date.submittedAugust 2012en
dc.date.updated2012-11-20T15:05:25Zen
dc.descriptiontexten
dc.description.abstractThis thesis introduces the infinitesimal symmetries of Dixmier-Douady gerbes over smooth manifolds. The collection of these symmetries are the counterpart for gerbes of the Lie algebra of circle invariant vector fields on principal circle bundles, and are intimately related to connective structures and curvings. We prove that these symmetries possess a Lie 2-algebra structure, and relate them to equivariant gerbes via a "differentiation functor". We also explain the relationship between the infinitesimal symmetries of gerbes and other mathematical structures including Courant algebroids and the String Lie 2-algebra.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2012-08-6066en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2012-08-6066en
dc.language.isoengen
dc.subjectGerbesen
dc.subjectLie 2-algebrasen
dc.subjectCategory theoryen
dc.subjectGeometryen
dc.titleInfinitesimal symmetries of Dixmier-Douady gerbesen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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