Revista Matemática Iberoamericana


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Volume 26, Issue 3, 2010, pp. 729–798
DOI: 10.4171/RMI/616

Published online: 2010-12-31

Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases

Takeshi Isobe[1]

(1) Tokyo Institute of Technology, Japan

We define various classes of Sobolev bundles and connections and study their topological and analytical properties. We show that certain kinds of topologies (which depend on the classes) are well-defined for such bundles and they are stable with respect to the natural Sobolev topologies. We also extend the classical Chern-Weil theory for such classes of bundles and connections. Applications related to variational problems for the Yang-Mills functional are also given.

Keywords: Sobolev bundle, topology of bundle, Yang-Mills functional, variational problem

Isobe Takeshi: Topological and analytical properties of Sobolev bundles. II. Higher dimensional cases. Rev. Mat. Iberoamericana 26 (2010), 729-798. doi: 10.4171/RMI/616