Group Actions and Groupoids
The notion of group action can be put in a broader context by using the action groupoid associated to the group action, thus allowing techniques from groupoid theory such as presentations and fibrations. Further the stabilisers of the action are the vertex groups, and the orbits of the action are the components, of the action groupoid. For more details, see the book Topology and groupoids referenced below.
This action groupoid comes with a morphism which is a covering morphism of groupoids. This allows a relation between such morphisms and covering maps in topology.
Read more about this topic: Group Action
Famous quotes containing the words group and/or actions:
“There is nothing in the world that I loathe more than group activity, that communal bath where the hairy and slippery mix in a multiplication of mediocrity.”
—Vladimir Nabokov (1899–1977)
“Only the actions of the just
Smell sweet and blossom in their dust.”
—James Shirley (1596–1666)