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? 



homological 2 dimensional groups
See my paper with Bruce Kleiner "Geometry of quasiplanes" for general unital commutative rings, it also contains a reference to the paper by Eckmann and Linnell from 1983 where they prove the theorem for PD(2) groups over Z and to the one by Bowditch which works over Q.


