Global Polyfold Fredholm setup
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EP-groupoid basics
A polyfold should be an "M-polyfold with isotropy". This is implemented via the language of EP-groupoids, which in finite dimensions reduce to orbifolds. First, recall that a groupoid is a small category in which every morphism is invertible (hence a groupoid with a single object is the same thing as a group). Now define an EP-groupoid to be a groupoid with morphism set satisfying these properties:
- (Lie) and are equipped with M-polyfold structures, with respect to which the source, target, multiplication, unit, and inversion maps
are sc-smooth.
- (etale) and are surjective local sc-diffeomorphisms.
- (proper) For every , there exists a neighborhood so that is proper.
Example: We work out the EP-groupoid structure of in detail.
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