= Covering homomorphism
A covering homomorphism is a <surjective group homomorphism> between <topological groups> whose underlying map is a <covering map>. Its <group kernel> is the discrete <fibre> above the <identity element>. Group <translations> identify every other <fibre> with a <coset> of that <group kernel>.
For example, the <group homomorphism> $\mathbb R\to S^1$, $t\mapsto e^{2\pi it}$, is a <covering map> from the additive <real numbers> to the <circle group>, with <group kernel> $\mathbb Z$. Small open arcs lift to disjoint intervals, while adding an <integer> moves between the sheets. A <surjective group homomorphism> alone need not be a <covering map>; the local-sheet condition is additional topological information.
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