G-Man (slang) 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 Independence (1919-1921). According to the "Merriam-Webster
(G,X)-manifold (G,X)-manifold If X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structures are always manifolds and are called (G, X)-manifolds. This notion is often used with G being a Lie group and X a homogeneous space for G. Foundational examples are hyperbolic manifolds and affine manifolds. Let formula_1 be a connected differential manifold and formula_2 be a subgroup of the group of diffeomorphisms of formula_1