 K-theory Gysin sequence of a sphere bundle

ID: k-theory-gysin-sequence-of-a-sphere-bundle

S (E) \to D (E) \to Th (E)

and the Thom isomorphism give

\dots \to K^{i} (X) \cdot e^{K} (E) K^{i} (X) p^{*} K^{i} (S (E)) p_{!} K^{i + 1} (X) \to \dots .

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