Quaternionic analytic torsion

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

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...

Geometry of Quaternionic Kähler connections with torsion

The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n).Sp(1), QKT-connection. We study the geometry of QKT-connections. We find conditions to the existence of a QKT-connection and prove that if it exists it is unique. Studying conformal transformations we obtain a lot of (c...

Analytic Torsion for Families

Refined analytic torsion

For a representation of the fundamental group of a compact oriented odd-dimensional manifold we define a refinement of the Ray-Singer torsion associated to this representation. If the representation is acyclic then our new invariant is a non-zero complex number, which can be viewed as an analytic counterpart of the refined combinatorial torsion introduced by Turaev. The refined analytic torsion...