Diagrammatically reducible group presentations and equations over groups

JONATHAN ARIEL BARMAK; ELIAS GABRIEL MINIAN

Valparaiso

Congreso; Primer Encuentro Conjunto: Sociedad de Matemática de Chile y Unión Matemática Argentina; 2016

SOMACHI y UMA

A group presentation P is said to be diagrammatically reducible (DR) if every tessellation of the sphere, with edges labeled by generators of P and faces corresponding to relators, has two faces which are symmetric across a comon edge. In this case, a result of S. Gersten says that any system of equations modeled by P, over any group G, has a solution in an overgroup of G. In this talk we will present a test for deciding diagrammatic reducibility and we will use it to solve some equations in two variables. This is part of a joint work with G. Minian.