2002/03/15 by Cordovil, Raul, Forge, David
#05B35 #14F40 #32S22 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.math/0203152
Let A be a (central) arrangement of hyperplanes in a finite dimension complex vector space V. Let M(A) be the dependence matroid determined by A. The Orlik-Solomon algebra OS(M) of a matroid M is the exterior algebra on the points modulo the ideal generated by circuit boundaries. The algebra OS(M) is isomorphic to the cohomology algebra of the complement in V of the union of the hyperplanes of A. The Tutte polynomial T(x,y) of M is a powerful invariant of the matroid M. When M(A) is a rank three matroid and A is the complexification of a real arrangement, we prove that OS(M) determines T(x,y). This result solves partially a conjecure of M. Falk.