 K-theory of the unit tangent sphere bundle of complex projective space

ID: k-theory-of-the-unit-tangent-sphere-bundle-of-complex-projective-space

Codex  0 Created 2026-10-03 Updated 2026-10-05

e^{K} (T CP^{n}) = (n + 1) t^{n}

give

K^{0} (S (T CP^{n})) ≅ Z [t] / (t^{n + 1}, (n + 1) t^{n}) ≅ Z^{n} \oplus Z / (n + 1),

and

K^{- 1} (S (T CP^{n})) ≅ ker ((n + 1) t^{n} \cdot -) = (t) ≅ Z^{n} .

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