Kulkarni limit sets for cyclic quaternionic projective groups

TL;DR

This paper computes the Kulkarni limit sets for cyclic subgroups of the quaternionic projective linear group acting on quaternionic projective space.

Contribution

It provides the first explicit computation of Kulkarni limit sets for cyclic subgroups in the quaternionic setting.

Findings

Kulkarni limit sets are explicitly characterized for cyclic subgroups.

The results extend understanding of group actions on quaternionic projective spaces.

New techniques for computing limit sets in quaternionic geometry are introduced.

Abstract

We consider the natural action of the quaternionic projective linear group $\mathrm{PSL}(n+1,\mathbb{H})$ on the quaternionic projective space $\mathbb{P}^n_{\mathbb{H}}$. We compute the Kulkarni limit sets for the cyclic subgroups of $\mathrm{PSL}(n+1,\mathbb{H})$.