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Conference Paper: Analytic torsion of Z2-graded elliptic complexes
Title | Analytic torsion of Z2-graded elliptic complexes |
---|---|
Authors | |
Issue Date | 2011 |
Publisher | American 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/224178 |
ISBN | |
ISSN | 2023 SCImago Journal Rankings: 0.322 |
DC Field | Value | Language |
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dc.contributor.author | Mathai, V | - |
dc.contributor.author | Wu, S | - |
dc.date.accessioned | 2016-03-29T04:13:19Z | - |
dc.date.available | 2016-03-29T04:13:19Z | - |
dc.date.issued | 2011 | - |
dc.identifier.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 | - |
dc.identifier.isbn | 9780821849446 | - |
dc.identifier.issn | 0271-4132 | - |
dc.identifier.uri | http://hdl.handle.net/10722/224178 | - |
dc.description.abstract | We 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.language | eng | - |
dc.publisher | American Mathematical Society. | - |
dc.relation.ispartof | Contemporary Mathematics | - |
dc.rights | First published in [Publication] in [volume and number, or year], published by the American Mathematical Society | - |
dc.title | Analytic torsion of Z2-graded elliptic complexes | - |
dc.type | Conference_Paper | - |
dc.identifier.email | Wu, S: swu@maths.hku.hk | - |
dc.identifier.authority | Wu, S=rp00814 | - |
dc.identifier.hkuros | 172987 | - |
dc.identifier.volume | 546 | - |
dc.identifier.spage | 199 | - |
dc.identifier.epage | 212 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0271-4132 | - |