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Inner structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">Spin</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mn>4</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> gauge potential on 4-dimensional manifolds