On the n-transitivity of the group of Möbius transformations on C∞

Abstract

Mobius transformations generate the conformal group in the plane and have been used in neural networks and conformal field theory. Sonic invariant characteristic properties of Mobius transformations such as the invariance of cross-ratio of four distinct points oil the extended complex plane C-infinity = C boolean OR {infinity} under a Mobius transformation, have many applications. We consider the geometric interpretation of the notion of n-transitivity of the group of Mobius transformations oil the extended complex plane C-infinity We see that this notion is closely related to the invariant characteristic properties of Mobius transformations and the notion of cross-ratio.