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:
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—Simone Weil (19101943)
“Therefore all just persons are satisfied with their own praise. They refuse to explain themselves, and are content that new actions should do them that office. They believe that we communicate without speech, and above speech, and that no right action of ours is quite unaffecting to our friends, at whatever distance; for the influence of action is not to be measured by miles.”
—Ralph Waldo Emerson (18031882)