On connectedness of chaotic sections of some 3-periodic surfaces
  In the present paper we construct a Z^{3}-periodic surface in R^{3} whose almost all plane sections of a certain direction consist of exactly one connected component. This question originates from a problem of Novikov on the semi- classical motion of an electron in strong magnetic field. Our main tool is the Rips machine algorighm for band complexes. 
Alexandra Skripchenko
math.GT math.DS