Subject: Question on orbi-CW-complexes From: Gabriele Mondello Date: Fri, 9 Dec 2005 22:58:52 -0500 (EST) Hi, I am having some trouble in giving a reasonable definition of an orbi-CW-complex. The main problem is that an orbifold is described by local conditions, while a CW-complex structure is not a local fact. Also, I can define an orbifold a little more "globally" as a topological groupoid X=(X_0,X_1) with X_0,X_1 manifolds, and smooth maps s,t:X_1--->X_0 source and target, u:X_0--->X_1 unit, i:X_1--->X_1 inverse and m=composition; requiring that s,t are local diffeomorphisms and (s,t):X_1--->X_0xX_0 is proper (I want finite stabilizers). I suspect that for an orbi-CW-complex I should drop the condition "s,t local homeomorphisms" and ask something like "X_0,X_1 are CW-complexes and s,t are cellular maps, composition of a local homeomorphism and a closed embedding". Still I think someone should have already given such a definition. Does anyone know any reference? Gabriele Mondello