section_path: Contemporary geometry/Geometric group theory
section_name: Geometric group theory
paragraph_text: Geometric group theory
  
  Geometric group theory uses large-scale geometric techniques to study finitely generated groups. It is closely connected to low-dimensional topology, such as in Grigori Perelman 's proof of the Geometrization conjecture, which included the proof of the Poincaré conjecture, a Millennium Prize Problem.
  
  Geometric group theory often revolves around the Cayley graph, which is a geometric representation of a group. Other important topics include quasi-isometries, Gromov-hyperbolic groups, and right angled Artin groups.