On a notion of maps between orbifolds, I. function spaces

Details On a notion of maps between orbifolds, I. function spaces On a notion of maps between orbifolds, I. function spaces

2006-03-29

arxiv.org/abs/math/0603671v1

Communications in Contemporary Mathematics {\bf 8} no.5 (2006), 569-620

Mathematics

Geometric Topology

Final version, 46 pages. Accepted for publication in Communications in Contemporary Mathematics. A preliminary version of this

Scientific paper

This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the topological structure of the space of such maps. In particular, we show that the space of such maps of C^r-class between smooth orbifolds has a natural Banach orbifold structure if the domain of the map is compact, generalizing the corresponding result in the manifold case. Motivations and applications of the theory come from string theory and the theory of pseudoholomorphic curves in symplectic orbifolds.

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