In a  Commentarii Mathematici Helvetici paper  by Benno Eckman  and Heinz  Müller in  1980 (volume  50,  pages 510-520) proved  that poincaré Duality  Groups  of  dimension 2  with  positive first Betti  number  are  surface  groups. 

Is  there any  development  into  proving  that certain groups  of   (homological) or  geometric dimension  2  are surface  groups?