Topology of spaces of S-immersions
  We use the wrinkling theorem proven in Y. Eliashberg and N. Mishachev, "Wrinkling of smooth mappings and its applications - I", Invent. Math., 130(1997), 345-369, to fully describe the homotopy type of the space of S-immersions, i.e. equidimensional folded maps with prescribed folds. 
Yakov M. Eliashberg, Nikolai M. Mishachev
math.GT