Refined analytic torsion as analytic function on the representation variety and applications
arXiv:1307.4912 · doi:10.1007/s40316-016-0062-x
Abstract
We prove that refined analytic torsion on a manifold with boundary is an analytic section of the determinant line bundle over the representation variety. As a fundamental application we establish a gluing formula for refined analytic torsion on connected components of the complex representation space which contain a unitary point. Finally we provide a new proof of Bruening-Ma gluing formula for the Ray-Singer torsion associated to a non-Hermitian connection. Our proof is quite different from the one given by Bruening and Ma and uses a temporal gauge transformation.
37 pages, several important changes suggested by the referee