In the mathematical theory of Kleinian groups, the Riley slice of Schottky space is a family of Kleinian groups generated by two parabolic elements. It was studied in detail by Keen & Series (1994), and some subtle errors in their paper were corrected by Komori & Series (1998).
Definition
The Riley slice consists of the complex numbers ρ such that the two matrices
generate Kleinian group G with regular set Ω such that Ω/G is a 4-times punctured sphere.
The Riley slice is the quotient of the Teichmuller space of a 4-times punctured sphere by a group generated by Dehn twists around a curve, and so is topologically an annulus.
References
Riley slice Wikipedia(Text) CC BY-SA