Scattering matrix and analytic torsion

Analytic Surgery and Analytic Torsion

Analytic surgery, as defined in [9] and [6], is a one-parameter metric deformation of a Riemannian manifold M , which stretches M across a separating hypersurface H in a cylindrical fashion; the singular limit is a complete manifold with asymptotically cylindrical ends, M . In this paper, the analysis of [9] and [6] is used to study the behaviour of analytic torsion of unitary representations u...

Enriques Surfaces and Analytic Torsion

In a series of works [Bo3-5], Borcherds developed a theory of modular forms over domains of type IV which admits an infinite product expansion. Among such modular forms, Borcherds’s Φ-function ([Bo4]) has an interesting geometric background; It is a modular form on the moduli space of Enriques surfaces characterizing the discriminant locus. In his construction, Φ-function is obtained as the den...

2 Analytic and Reidemiester Torsion

We extend the deenition of analytic and Reidemeister torsion from closed compact Riemannian manifolds to compact Riemannian manifolds with bound

Analytic Torsion for Families

Quaternionic analytic torsion

We define an (equivariant) quaternionic analytic torsion for antiselfdual vector bundles on quaternionic Kähler manifolds, using ideas by Leung and Yi. We compute this torsion for vector bundles on quaternionic homogeneous spaces with respect to any isometry in the component of the identity, in terms of roots and Weyl groups. 2000 Mathematics Subject Classification: 53C25, 58J52, 53C26, 53C35