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Algebra and Geometry Seminar

Thursday, February 29, 2024
3:45pm to 5:00pm
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Enumerating stably trivial topological vector bundles with higher real K-theories
Morgan Opie, Mathematics Department, UCLA,

USC, Kaprelian Hall room 414

The zeroeth complex topological K-theory of a space encodes complex vector bundles up to stabilization. Since complex topological K-theory is highly computable, this is a great place to start when asking questions about topological vector bundles. But, in general, there are many non-equivalent vector bundles with the same K-theory class. Bridging the gap between K-theory and actual bundle theory is challenging, even for the simplest CW complexes.

Building on work of Hu, we use Weiss calculus and a little chromatic homotopy theory to translate vector bundle enumeration questions to tractable stable homotopy theory computations. We compute lower bounds for the number of stably trivial rank complex rank r topological vector bundles on complex projective n-space, for infinitely many n and r. This is joint work with Hood Chatham and Yang Hu.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].