Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary

TL;DR

This paper confirms the infinitesimal rigidity of a specific compact hyperbolic 4-orbifold with totally geodesic boundary, supporting a broader conjecture for dimensions greater than three.

Contribution

It verifies Kerckhoff and Storm's conjecture for a particular 4-dimensional hyperbolic orbifold derived from the 120-cell.

Findings

Confirmed infinitesimal rigidity for the 4-dimensional hyperbolic 120-cell orbifold

Supports the conjecture that hyperbolic n-orbifolds with totally geodesic boundary are rigid for n>3

Provides a specific example validating the general rigidity conjecture

Abstract

Kerckhoff and Storm conjectured that compact hyperbolic n-orbifolds with totally geodesic boundary are infinitesimally rigid when n>3. This paper verifies this conjecture for a specific example based on the 4-dimensional hyperbolic 120-cell.