On the Burns-Epstein invariants of spherical CR 3-manifolds

TL;DR

This paper introduces a method to compute the Burns-Epstein invariant of spherical CR 3-manifolds from their holonomy representations, providing explicit formulas for certain Seifert fibered homology spheres.

Contribution

It develops a new computational approach for the Burns-Epstein invariant based on holonomy, applicable to spherical CR homology spheres and Seifert fibered cases.

Findings

Derived a formula for the Burns-Epstein invariant modulo an integer

Provided a method to compute the invariant from holonomy representations

Applied the method to specific classes of spherical CR 3-manifolds

Abstract

In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.