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Science China Mathematics

, Volume 53, Issue 3, pp 555–563 | Cite as

Twisted analytic torsion

  • Varghese Mathai
  • SiYe Wu
Open Access
Reviews

Abstract

We review the Reidemeister, Ray-Singer’s analytic torsion and the Cheeger-Müller theorem. We describe the analytic torsion of the de Rham complex twisted by a flux form introduced by the current authors and recall its properties. We define a new twisted analytic torsion for the complex of invariant differential forms on the total space of a principal circle bundle twisted by an invariant flux form. We show that when the dimension is even, such a torsion is invariant under certain deformation of the metric and the flux form. Under T-duality which exchanges the topology of the bundle and the flux form and the radius of the circular fiber with its inverse, the twisted torsion of invariant forms are inverse to each other for any dimension.

Keywords

analytic torsion circle bundles T-duality 

MSC(2000)

Primary 58J52 Secondary 57Q10, 58J40, 81T30 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of AdelaideAdelaideAustralia
  2. 2.Department of MathematicsUniversity of ColoradoBoulderUSA
  3. 3.Department of MathematicsUniversity of Hong KongHong KongChina

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