# Trace theorem for quasi-Fuchsian groups

## TL;DR

This paper completes the proof of the Trace Theorem within the framework of quantized calculus for quasi-Fuchsian groups, addressing a previously incomplete proof in noncommutative geometry.

## Contribution

It provides the full proof of the Trace Theorem for quasi-Fuchsian groups, advancing the mathematical understanding in noncommutative geometry.

## Key findings

- Complete proof of the Trace Theorem for quasi-Fuchsian groups
- Clarification of the theorem's role in noncommutative geometry
- Strengthened foundation for future research in the field

## Abstract

We complete the proof of the Trace Theorem in the quantized calculus for quasi-Fuchsian group which was stated and sketched, but not fully proved, on pp. 322-325 in the book "Noncommutative Geometry" of the first author.