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2024-09-25 18:06:15 UTC

Diffgeometer1 on Nostr: The index of a vector field is defined in terms of isolated zeros of the vector ...

The index of a vector field is defined in terms of isolated zeros of the vector field.

If a vector field is nonvanishing, is the index defined to be zero trivially since it has no zeros and there is nothing to calculate?

A related question: does a manifold always admit a vector field with isolated zeros?