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I understand in mathematics there are many "quotienting " proceduce, is this the only reason that we consider equivariant theory for different "unequivariant" theory? Are there any more applications for equivariant theory?Thanks!

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    Frequently you're not interested in the quotient object, as you're viewing the action as a group of symmetries of something. More often one wants to know things like "is a component preserved by the group action?" "is there a fixed point?" etc. The quotient does not answer these questions.2010-10-08

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