Topological arguments for Kolmogorov complexity
  We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties. 
Alexander Shen (CNRS and LIRMM, France), Andrei Romashchenko (CNRS and   LIRMM, France)
cs.DM cs.CC cs.IT math.IT