Examples of non-flat bundles of rank one
Ananyo Dan, Agust\'in Romano-Vel\'azquez
TL;DR
This paper provides examples of line bundles on non-compact surfaces that do not admit flat connections, highlighting limitations in the geometric structure of such bundles.
Contribution
It introduces specific examples of non-flat line bundles on non-compact surfaces, illustrating the existence of bundles without flat connections.
Findings
Certain line bundles on non-compact surfaces cannot be equipped with flat connections
Examples demonstrate limitations of flat connection existence on non-compact surfaces
Highlights the distinction between flat and non-flat line bundles in geometric topology
Abstract
In this article we give several examples of line bundles on certain non-compact surfaces that cannot be equipped with a flat connection.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry