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Geometry & Topology Seminar

Title: Approximation of weak G-bundles in high dimensions
Speaker: Swarnendu Sil (ETH Zurich)
Date: 09 March 2020
Time: 4:00 pm
Venue: LH-1, Mathematics Department

The analysis for Yang-Mills functional and in general, problems related to higher dimensional gauge theory, often requires one to work with weak notions of principal G-bundles and connections on them. The bundle transition functions for such bundles are not continuous and thus there is no obvious notion of a topological isomorphism class.

In this talk, we shall discuss a few natural classes of weak bundles with connections which can be approximated in the appropriate norm topology by smooth connections on smooth bundles. We also show how we can associate a topological isomorphism class to such bundle-connection pairs, which is invariant under weak gauge changes. In stark contrast to classical notions, this topological isomorphism class is not independent of the connection.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 03 Feb 2023