Decision problems for 3-manifolds and their fundamental groups
  We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold groups. 
Matthias Aschenbrenner, Stefan Friedl and Henry Wilton
math.GT math.GR