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:
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)
“When posterity judges our actions here it will perhaps see us not as unwilling prisoners but as men who for whatever reason preferred to remain non-contributing individuals on the edge of society.”
—George Lucas (b. 1944)