A note on stable commutator length in braided Ptolemy-Thompson groups

TL;DR

This paper demonstrates that the stable commutator lengths in braided Ptolemy-Thompson groups are precisely the non-negative rational numbers, revealing a clear structure of these algebraic invariants.

Contribution

It establishes that the set of all stable commutator lengths in these groups equals the non-negative rationals, providing a complete characterization.

Findings

Stable commutator lengths are non-negative rationals.

The set of stable commutator lengths is fully characterized.

Provides insight into the algebraic structure of braided Ptolemy-Thompson groups.

Abstract

In this note, we show that the sets of all stable commutator lengths in the braided Ptolemy-Thompson groups are equal to non-negative rational numbers.