Moves on Pseudoline Diagrams

Pseudoline diagrams are simple arrangements of pseudolines in the affine plane where at each vertex one indicates which pseudolinecrosses overthe other. They naturally appear as projections of configurations of lines in 3-space. Motivated by isotopies of these spatial configurations, we define an equivalence for diagrams, generated by two types of moves. We encode diagrams by words and consider the associated word problem. Furthermore, in this combinational framework we obtain two new results on thechiralityof triples of lines, which are useful in the study of isotopies of line configurations in 3-space.