Lecture 6: Paper folding: overview, definitions, connectivity, 1D flat foldability, 2D map folding
Page 3: Definitions: folded-state order (continued), noncrossing condition, folded state, folding motion. Connectivity: every folded state can be reached by a folding motion; proof sketch.
You can view the paper by Demaine, Devadoss, Mitchell, O'Rourke on definitions of folding and connectivity of the configuration space. The definition here is slightly different from the one presented in the paper, allowing more general pieces of paper and arbitrary dimension, and a cleaner noncrossing condition.
These are rough, personal lecture notes handwritten by Erik Demaine used during lecture. Their primary purpose is for reading/review by students of the class.