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I'm doing a class on K-Theory, and I'm confused about what the support of a complex of vector bundles is. Consider the following complex: $$0\to V_1\to V_2\to \dots\to V_n\to 0$$ Assume that all vector bundles have been defined on the same manifold $M$.

Is the support of this vector bundle complex just the set of points on $M$ where the fiber of each vector bundle in this complex is non-zero?

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The support of a complex of vector bundles usually refers to the set of points at which it is not exact. That is, the support is the set of $x\in M$ such that the complex of fibers $$0\to (V_1)_x\to (V_2)_x\to \dots\to (V_n)_x\to 0$$ is not exact.

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