math214:02-19
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math214:02-19 [2020/02/19 09:33] pzhou |
math214:02-19 [2026/02/21 14:41] (current) |
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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 ===== | ||
math214/02-19.1582104824.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
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