2009/12/31 by Varghese Mathai, Siye Wu
Mathematics · Medicine · Physics and Astronomy · #Advanced Neuroimaging Techniques and Applications #Advanced Operator Algebra Research #Bundle #Geometry #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #Torsion (gastropod) #hep-th #math.DG #msc:57Q10 #msc:58J40 #msc:58J52 #msc:81T30.
paper · pdf · doi:10.1007/s11425-010-0053-3
published as Sci China Math 53 (2010) 555--563 · 10 pages, based on a talk at the International Conference on Complex Analysis and Related Topics, August 2009, Beijing, to appear in the special volume in honor of Prof. Yang Lo on the occasion of his 70th birthday; correction of typos and some other minor changes
arxiv created 2010/03/01 · openalex publication_date 2010/03/01 · arxiv updated 2010/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.