Certifying incompressibility of non-injective surfaces with scl

TL;DR

This paper constructs new examples of non-injective, incompressible surface group maps into PSL(2,C) using stable commutator length, providing simple certificates for their incompressibility.

Contribution

It introduces a method to certify incompressibility of non-injective surface group maps via stable commutator length, expanding known examples.

Findings

New examples of incompressible, non-injective surface group maps

Simple certificates for incompressibility derived from stable commutator length

Enhanced understanding of surface group representations into PSL(2,C)

Abstract

Cooper-Manning and Louder gave examples of maps of surface groups to PSL(2,C) which are not injective, but are incompressible (i.e. no simple loop is in the kernel). We construct more examples with very simple certificates for their incompressibility arising from the theory of stable commutator length.