Wiring diagrams usually serve as a tool in the study of arrangements of lines and pseudolines. Here we go in the opposite direction, using known properties of line arrangements to motivate certain equivalence relations and actions on sets of wiring diagrams, which preserve the incidence lattice and the fundamental groups of the affine and projective complements of the diagrams. These actions are used in [GTV] to classify real arrangements of up to 8 lines and show that in this case, the incidence lattice determines both the affine and the projective fundamental groups.
Bibliographical noteFunding Information:
1Partially supported by The Israel Science Foundation (Center for Excellence Program), by the Emmy Noether Institute for Mathematics and by the Minerva Foundation (Germany). The research was done during the Ph.D. studies of David Garber, under the supervision of Prof. Mina Teicher. 2Partially supported by the Edmund Landau Center for Research in Mathematical Analysis and Related Subjects.