File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Analytic torsion for twisted de Rham complexes

TitleAnalytic torsion for twisted de Rham complexes
Authors
Issue Date2011
PublisherLehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.html
Citation
Journal of Differential Geometry, 2011, v. 88 n. 2, p. 297-332 How to Cite?
AbstractWe define analytic torsion τ(X,ε,H) ∈ det H •(X,ε,H) for the twisted de Rham complex, consisting of the spaces of differential forms on a compact oriented Riemannian manifold X valued in a flat vector bundle ε, with a differential given by ∇ε + H Λ · , where ∇ε is a flat connection on ε, H is an odd-degree closed differential form on X, and H•(X, ε, H) denotes the cohomology of this ℤ2-graded complex. The definition uses pseudodifferential operators and residue traces. We show that when dim X is odd, τ(X, ε, H) is independent of the choice of metrics on X and ε and of the representative H in the cohomology class [H]. We define twisted analytic torsion in the context of generalized geometry and show that when H is a 3-form, the deformation H → H-dB, where B is a 2-form on X, is equivalent to deforming a usual metric g to a generalized metric (g,B). We demonstrate some basic functorial properties. When H is a top-degree form, we compute the torsion, define its simplicial counterpart, and prove an analogue of the Cheeger-Müller Theorem. We also study the twisted analytic torsion for T -dual circle bundles with integral 3- form fluxes.
Persistent Identifierhttp://hdl.handle.net/10722/156274
ISSN
2015 Impact Factor: 1.24
2015 SCImago Journal Rankings: 3.244
References

 

DC FieldValueLanguage
dc.contributor.authorMathai, Ven_US
dc.contributor.authorWu, Sen_US
dc.date.accessioned2012-08-08T08:41:08Z-
dc.date.available2012-08-08T08:41:08Z-
dc.date.issued2011en_US
dc.identifier.citationJournal of Differential Geometry, 2011, v. 88 n. 2, p. 297-332en_US
dc.identifier.issn0022-040Xen_US
dc.identifier.urihttp://hdl.handle.net/10722/156274-
dc.description.abstractWe define analytic torsion τ(X,ε,H) ∈ det H •(X,ε,H) for the twisted de Rham complex, consisting of the spaces of differential forms on a compact oriented Riemannian manifold X valued in a flat vector bundle ε, with a differential given by ∇ε + H Λ · , where ∇ε is a flat connection on ε, H is an odd-degree closed differential form on X, and H•(X, ε, H) denotes the cohomology of this ℤ2-graded complex. The definition uses pseudodifferential operators and residue traces. We show that when dim X is odd, τ(X, ε, H) is independent of the choice of metrics on X and ε and of the representative H in the cohomology class [H]. We define twisted analytic torsion in the context of generalized geometry and show that when H is a 3-form, the deformation H → H-dB, where B is a 2-form on X, is equivalent to deforming a usual metric g to a generalized metric (g,B). We demonstrate some basic functorial properties. When H is a top-degree form, we compute the torsion, define its simplicial counterpart, and prove an analogue of the Cheeger-Müller Theorem. We also study the twisted analytic torsion for T -dual circle bundles with integral 3- form fluxes.en_US
dc.languageengen_US
dc.publisherLehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.htmlen_US
dc.relation.ispartofJournal of Differential Geometryen_US
dc.titleAnalytic torsion for twisted de Rham complexesen_US
dc.typeArticleen_US
dc.identifier.emailWu, S:swu@maths.hku.hken_US
dc.identifier.authorityWu, S=rp00814en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-80053533685en_US
dc.identifier.hkuros212044-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-80053533685&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume88en_US
dc.identifier.issue2en_US
dc.identifier.spage297en_US
dc.identifier.epage332en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridMathai, V=35563226300en_US
dc.identifier.scopusauthoridWu, S=15830510400en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats