Covering group

In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and the covering map p : G → H is a continuous group homomorphism. The map p is called the covering homomorphism. A frequently occurring case is a double covering group, a topological double cover in which H has index 2 in G; examples include the spin groups, pin groups, and metaplectic groups.

Roughly explained, saying that for example the metaplectic group Mp_2n is a double cover of the symplectic group Sp_2n means that there are always two elements in the metaplectic group representing one element in the symplectic group.