Prime order birational diffeomorphisms of the sphere

TL;DR

This paper classifies conjugacy classes of prime order elements in the group of birational diffeomorphisms of the real sphere, providing parametrizations via moduli spaces.

Contribution

It offers a complete classification of prime order conjugacy classes in the birational diffeomorphism group of the sphere, with explicit parametrizations.

Findings

Classification of conjugacy classes achieved

Parametrizations by moduli spaces provided

Enhanced understanding of the structure of birational diffeomorphisms

Abstract

The aim of this paper is to give the classification of conjugacy classes of elements of prime order in the group of birational diffeomorphisms of the two-dimensional real sphere. Parametrisations of conjugacy classes by moduli spaces are presented.