Coherent orientations for periodic orbit problems in symplectic geometry.
A small perturbation method is developed and employed to construct frames with compactly supported elements of small shrinking support for Besov and Triebel-Lizorkin spaces in the general setting of a doubling metric measure space in the presence of a nonnegative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. This allows one, in particular, to construct compactly supported frames for Besov and Triebel-Lizorkin spaces on the sphere, on the interval with...
The refined analytic torsion associated to a flat vector bundle over a closed odd-dimensional manifold canonically defines a quadratic form on the determinant line of the cohomology. Both and the Burghelea-Haller torsion are refinements of the Ray-Singer torsion. We show that whenever the Burghelea-Haller torsion is defined it is equal to . As an application we obtain new results about the Burghelea-Haller torsion. In particular, we prove a weak version of the Burghelea-Haller conjecture relating...