Seeing as the tangent bundle of a manifold is an important object in differential geometry, I was wondering if it has any specific behavior in the K-theory of a manifold. (Either real/complex, reduced/otherwise I'm guessing it doesn't make a difference).
For example, does the tangent bundle generate an interesting ideal in the $K$-ring? Is it radical? Prime? Is it a nilpotent element?
2026-02-22 19:33:09.1771788789
How does the class of the tangent bundle behave in the K-theory ring?
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