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- $g_{\alpha \beta} \circ g_{\beta \alpha}=1_F$ over $U_\alpha \cap U_\beta$ | - $g_{\alpha \beta} \circ g_{\beta \alpha}=1_F$ over $U_\alpha \cap U_\beta$ | ||
- $g_{\alpha \beta} \circ g_{\beta\gamma} \circ g_{\gamma \alpha} = 1_F$ over $U_\alpha \cap U_\beta \cap U_\gamma$. | - $g_{\alpha \beta} \circ g_{\beta\gamma} \circ g_{\gamma \alpha} = 1_F$ over $U_\alpha \cap U_\beta \cap U_\gamma$. | ||
+ | |||
+ | ==== Example of Vector Bundles ==== | ||
+ | $E(n,k) \to Gr(n, k)$ tautological bundle over the Grassmannian. | ||
+ | |||
+ | $O(-1) \to \C\P(1)$. | ||
+ | |||
+ | ==== Operations on Vector Bundles ==== | ||
+ | Direct Sum, Tensor Product, Hom. | ||
+ | |||
===== Cotangent Bundle ===== | ===== Cotangent Bundle ===== |