Frontiers of sphere recognition in practice
  Sphere recognition is known to be undecidable in dimensions five and beyond, and no polynomial time method is known in dimensions three and four. Here we report on positive and negative computational results with the goal to explore the limits of sphere recognition from a practical point of view. An important ingredient are randomly constructed discrete Morse functions. 
Michael Joswig, Davide Lofano, Frank H. Lutz, Mimi Tsuruga
math.GT cs.CG math.AT math.MG