2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226135We give a new proof of the theorem of Krstic-McCool from the title. Our proof has potential applications to the study of finiteness properties of other subgroups of SL_2 resulting from rings of functions on curves.This is the version published by Algebraic & Geometric Topology on 11 July 2006Group Theory20F05, 20F65A geometric proof that SL_2(Z[t,t^-1]) is not finitely presentedtext