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:
“A little group of willful men, representing no opinion but their own, have rendered the great government of the United States helpless and contemptible.”
—Woodrow Wilson (1856–1924)
“There is a Book
By seraphs writ with beams of heavenly light,
On which the eyes of God not rarely look,
A chronicle of actions just and bright—
There all thy deeds, my faithful Mary, shine;
And since thou own’st that praise, I spare thee mine.”
—William Cowper (1731–1800)