Twisted Analytic Torsion

Details Twisted Analytic Torsion Twisted Analytic Torsion

2009-12-11

arxiv.org/abs/0912.2184v2

Sci China Math 53 (2010) 555--563

Mathematics

Differential Geometry

10 pages, based on a talk at the International Conference on Complex Analysis and Related Topics, August 2009, Beijing, to app

Scientific paper

10.1007/s11425-010-0053-3

We review the Reidemeister torsion, Ray-Singer's analytic torsion and the Cheeger-M"uller 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 torsions of invariant forms are inverse to each other for any dimension.

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