Orbifold chart.

Question

i'm trying to define an orbifold chart for the teardrop $R^2/Z_2$, where $Z_2$ acts via rotations. My advisor gave a tip: to use stereographic projections. But I'm a little stuck. Any help?

Answer 1

Here's a wordy hint. The purpose of an orbifold is to capture the notion of "looks locally like a quotient." Towards this end, you can think of an orbifold chart as a map to the quotient of a manifold chart by a finite group action stabilizing 0 etc. (For ordinary manifold points in the orbifold, the finite group is trivial.)

Now do you see what to do?