Characteristic Classes of the Boundary of a Complex b-manifold

Abstract

We prove a classification theorem by cohomology classes for compact Riemannian manifolds with a one-parameter group of isometries without fixed points generalizing the classification of line bundles (more precisely, their circle bundles) over compact manifolds by their first Chern class. We also prove a classification theorem generalizing that of holomorphic line bundles over compact complex manifold by the Picard group of the base for a subfamily of manifolds with additional structure resembling that of circle bundles of such holomorphic line bundles.