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Article: Analytic torsion for twisted de Rham complexes
Title  Analytic torsion for twisted de Rham complexes 

Authors  
Issue Date  2011 
Publisher  Lehigh 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. 297332 How to Cite? 
Abstract  We 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 odddegree closed differential form on X, and H•(X, ε, H) denotes the cohomology of this ℤ2graded 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 3form, the deformation H → HdB, where B is a 2form 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 topdegree form, we compute the torsion, define its simplicial counterpart, and prove an analogue of the CheegerMüller Theorem. We also study the twisted analytic torsion for T dual circle bundles with integral 3 form fluxes. 
Persistent Identifier  http://hdl.handle.net/10722/156274 
ISSN  2015 Impact Factor: 1.24 2015 SCImago Journal Rankings: 3.244 
References 
DC Field  Value  Language 

dc.contributor.author  Mathai, V  en_US 
dc.contributor.author  Wu, S  en_US 
dc.date.accessioned  20120808T08:41:08Z   
dc.date.available  20120808T08:41:08Z   
dc.date.issued  2011  en_US 
dc.identifier.citation  Journal of Differential Geometry, 2011, v. 88 n. 2, p. 297332  en_US 
dc.identifier.issn  0022040X  en_US 
dc.identifier.uri  http://hdl.handle.net/10722/156274   
dc.description.abstract  We 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 odddegree closed differential form on X, and H•(X, ε, H) denotes the cohomology of this ℤ2graded 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 3form, the deformation H → HdB, where B is a 2form 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 topdegree form, we compute the torsion, define its simplicial counterpart, and prove an analogue of the CheegerMüller Theorem. We also study the twisted analytic torsion for T dual circle bundles with integral 3 form fluxes.  en_US 
dc.language  eng  en_US 
dc.publisher  Lehigh University, Dept of Mathematics. The Journal's web site is located at http://www.lehigh.edu/~math/jdg.html  en_US 
dc.relation.ispartof  Journal of Differential Geometry  en_US 
dc.title  Analytic torsion for twisted de Rham complexes  en_US 
dc.type  Article  en_US 
dc.identifier.email  Wu, S:swu@maths.hku.hk  en_US 
dc.identifier.authority  Wu, S=rp00814  en_US 
dc.description.nature  link_to_subscribed_fulltext  en_US 
dc.identifier.scopus  eid_2s2.080053533685  en_US 
dc.identifier.hkuros  212044   
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.080053533685&selection=ref&src=s&origin=recordpage  en_US 
dc.identifier.volume  88  en_US 
dc.identifier.issue  2  en_US 
dc.identifier.spage  297  en_US 
dc.identifier.epage  332  en_US 
dc.publisher.place  United States  en_US 
dc.identifier.scopusauthorid  Mathai, V=35563226300  en_US 
dc.identifier.scopusauthorid  Wu, S=15830510400  en_US 