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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Showing an Ext^2 element is zero
If we have an extension of bundles $0 \to E \to F \to G \to 0$ on $X$, then to show that this is the zero element in $Ext^1_X(G,E)$, we need to show that this sequence splits. To produce a splitting …