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=== What is $$F_A$$ geometrically? ===
=== What is $$F_A$$ geometrically? ===
[https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_theorem Atiyah-Singer index theorem]
 
$$F_A$$ is the curvature tensor associated to the connection or vector potential $$A$$.


=== What are $$R_{\mu v}$$ and $$R$$ geometrically? ===  
=== What are $$R_{\mu v}$$ and $$R$$ geometrically? ===  
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