Affine twist deformation of a sphere with holes

TL;DR

This paper introduces the affine twist parameter for affine deformations of a sphere with holes, establishing a parametrization of the deformation space analogous to Fenchel-Nielsen twists in Teichmüller theory.

Contribution

It defines a new affine twist parameter and shows how the affine deformation space can be parametrized by Margulis invariants and this new parameter.

Findings

Affine twist parameter is canonically related to Fenchel-Nielsen twist.

Deformation space parametrized by Margulis invariants and affine twist.

Provides a new perspective on affine deformations of punctured spheres.

Abstract

In this paper, we introduce a new parameter, the affine twist parameter for the affine deformation of a sphere with holes. We show that the affine deformation space can be parametrized by Margulis invariants and affine twist parameters. The affine twist parameter is canonically regarded as a correspondence to the Fenchel-Nielsen twist parameter in Teichmuller theory.