Classes of wiring diagrams and their invariants

Details Classes of wiring diagrams and their invariants Classes of wiring diagrams and their invariants

2001-07-24

arxiv.org/abs/math/0107178v1

J. Knot Theory Rami. 11(8), 1165--1191 (2002)

Mathematics

Algebraic Geometry

26 pages, 34 figures. Submitted

Scientific paper

Wiring diagrams usually serve as a tool in the study of arrangements of lines and pseudolines. In this paper 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.

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