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The Stratified Structure Of Spaces Of Smooth Orbifold Mappings, Joseph E. Borzellino, Victor Brunsden

Mathematics

We consider four notions of maps between smooth C^∞ orbifolds , with compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between and with the C^r topology carries the structure of a smooth C^∞ Banach (r finite)/Fréchet (r = ∞) manifold. For the notion of complete reduced orbifold map, the corresponding set of C^r maps between and with the C^r topology carries the …