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.
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Mathematics Subject Classification (2000)
The final version of this paper was written while the author was visiting the Department of Mathematics at the University of São Carlos, Brazil, financed by a grant from FAPESP. IIe gratefully acknowledges their hospitality.
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Dedicated to Linda P. Rothschild
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Mendoza, G.A. (2010). Characteristic Classes of the Boundary of a Complex b-manifold. In: Complex Analysis. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0009-5_15
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DOI: https://doi.org/10.1007/978-3-0346-0009-5_15
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0008-8
Online ISBN: 978-3-0346-0009-5
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