sentences:  Borel conjecture
  
  In mathematics, specifically geometric topology, the Borel conjecture (named for Armand Borel) asserts that an aspherical closed manifold is determined by its fundamental group, up to homeomorphism.It is a rigidity conjecture, demanding that a weak, algebraic notion of equivalence (namely, a homotopy equivalence) imply a stronger, topological notion (namely, a homeomorphism).