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:
“[The Republicans] offer ... a detailed agenda for national renewal.... [On] reducing illegitimacy ... the state will use ... funds for programs to reduce out-of-wedlock pregnancies, to promote adoption, to establish and operate children’s group homes, to establish and operate residential group homes for unwed mothers, or for any purpose the state deems appropriate. None of the taxpayer funds may be used for abortion services or abortion counseling.”
—Newt Gingrich (b. 1943)
“When a man’s life is destroyed or damaged by some wound or privation of soul or body, which is due to other men’s actions or negligence, it is not only his sensibility that suffers but also his aspiration toward the good. Therefore there has been sacrilege towards that which is sacred in him.”
—Simone Weil (1909–1943)