G-Man (slang) the Movie of the same name. G-Man (slang) G-Man (short for "Government Man") is an American slang term for special agents of the United States Government. It is specifically used as a term for a Federal Bureau of Investigation (FBI) agent. "G-Man" is also a term used for members of G Division, essentially a British anti-rebel police unit operating out of Dublin Castle prior to Irish Independence in 1922. Colonel Ned Broy uses the term in his official testimony for the Irish Army's Bureau of Military History in their archive of the Easter Rising (1916) and the Irish War of
G-structure on a manifold misleading: it suggests that "H" is a subgroup of "G", which is often the case, but need not be (for example for spin structures): it's properly called a lifting. More abstractly, ""G"-bundles over "X"" is a functor in "G": given a map "H" → "G", one gets a map from "H"-bundles to "G"-bundles by inducing (as above). Reduction of the structure group of a "G"-bundle "B" is choosing an "H"-bundle whose image is "B". The inducing map from "H"-bundles to "G"-bundles is in general neither onto nor one-to-one, so the structure group cannot always be reduced, and when it can,