Certifying incompressibility of noninjective surfaces with scl

Danny Calegari

Vol. 262 (2013), No. 2, 257–262

DOI: 10.2140/pjm.2013.262.257

Abstract

Cooper and Manning (2011) and Louder (2011) 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.

Keywords

simple loop conjecture, stable commutator length, compressible, PSL(2,C)

Mathematical Subject Classification 2010

Primary: 20F12, 57M60

Milestones

Received: 4 May 2012

Revised: 3 October 2012

Accepted: 19 October 2012

Published: 16 April 2013