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Conference Paper: Analytic torsion of Z2-graded elliptic complexes

TitleAnalytic torsion of Z2-graded elliptic complexes
Authors
Issue Date2011
PublisherAmerican Mathematical Society.
Citation
Noncommutative Geometry and Global Analysis - Conference in Honor of Henri Moscovici, Bonn, Germany, 29 June - 4 July 2009. In Contemporary Mathematics, 2011, v. 546, p. 199-212 How to Cite?
AbstractWe define analytic torsion of Z2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analytic and twisted holomorphic torsions, etc. The definition uses pseudo-differential operators and residue traces. We also study properties of analytic torsion for Z2-graded elliptic complexes, including the behavior under variation of the metric. For compact odd dimensional manifolds, the analytic torsion is independent of the metric, whereas for even dimensional manifolds, a relative version of the analytic torsion is independent of the metric. Finally, the relation to topological field theories is studied.
Persistent Identifierhttp://hdl.handle.net/10722/224178
ISBN
ISSN

 

DC FieldValueLanguage
dc.contributor.authorMathai, V-
dc.contributor.authorWu, S-
dc.date.accessioned2016-03-29T04:13:19Z-
dc.date.available2016-03-29T04:13:19Z-
dc.date.issued2011-
dc.identifier.citationNoncommutative Geometry and Global Analysis - Conference in Honor of Henri Moscovici, Bonn, Germany, 29 June - 4 July 2009. In Contemporary Mathematics, 2011, v. 546, p. 199-212-
dc.identifier.isbn9780821849446-
dc.identifier.issn0271-4132-
dc.identifier.urihttp://hdl.handle.net/10722/224178-
dc.description.abstractWe define analytic torsion of Z2-graded elliptic complexes as an element in the graded determinant line of the cohomology of the complex, generalizing most of the variants of Ray-Singer analytic torsion in the literature. It applies to a myriad of new examples, including flat superconnection complexes, twisted analytic and twisted holomorphic torsions, etc. The definition uses pseudo-differential operators and residue traces. We also study properties of analytic torsion for Z2-graded elliptic complexes, including the behavior under variation of the metric. For compact odd dimensional manifolds, the analytic torsion is independent of the metric, whereas for even dimensional manifolds, a relative version of the analytic torsion is independent of the metric. Finally, the relation to topological field theories is studied.-
dc.languageeng-
dc.publisherAmerican Mathematical Society.-
dc.relation.ispartofContemporary Mathematics-
dc.rightsFirst published in [Publication] in [volume and number, or year], published by the American Mathematical Society-
dc.titleAnalytic torsion of Z2-graded elliptic complexes-
dc.typeConference_Paper-
dc.identifier.emailWu, S: swu@maths.hku.hk-
dc.identifier.authorityWu, S=rp00814-
dc.identifier.hkuros172987-
dc.identifier.volume546-
dc.identifier.spage199-
dc.identifier.epage212-
dc.publisher.placeUnited States-

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