TOPOLOGICAL INVARIANCE OF INTERSECTION LATTICES OF ARRANGEMENTS IN CP(2)

Let A = {l1, l2, ..., l(n)} be a line arrangement in CP2, i.e., a col lection of distinct lines in CP2. Let L(A) be the set of all intersec tions of elements of A partially ordered by X less-than-or-equal-to Y double-line arrow pointing left and right Y subset-or-equal-to X. Let M(A) be CP2 - or A* where or A* = or{l(i): 1 less-than-or-equal-to i less-than-or-equal-to n}. The central problem of the theory of arrang ement of lines in CP2 is the relationship between M(A) and L(A*).