Local rigidity in quaternionic hyperbolic space

TL;DR

This paper investigates the deformation properties of quaternionic hyperbolic lattices, establishing local rigidity results and highlighting the greater flexibility of surface groups in quaternionic hyperbolic planes compared to complex hyperbolic planes.

Contribution

It proves local rigidity for quaternionic hyperbolic lattices and demonstrates increased flexibility of surface groups in quaternionic hyperbolic planes.

Findings

Quaternionic hyperbolic lattices exhibit local rigidity.

Surface groups are more flexible in quaternionic hyperbolic plane.

Differences in deformation behavior between quaternionic and complex hyperbolic spaces.

Abstract

In this note, we study deformations of quaternionic hyperbolic lattices in larger quaternionic hyperbolic spaces and prove local rigidity results. On the other hand, surface groups are shown to be more flexible in quaternionic hyperbolic plane than in complex hyperbolic plane.