Approximation of weak G-bundles in high dimensions
Swarnendu Sil, Forschungsinstitut fur Mathematik ETH Zurich
| Speaker |
Swarnendu Sil, Forschungsinstitut fur Mathematik ETH Zurich
|
|---|---|
| When |
Mar 05, 2020
from 04:00 PM to 05:00 PM |
| Where | LH 006 |
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Abstract: 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 Sobolev and Morrey-Sobolev 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.