The Topological And Combinatorial Properties Of A Class Of Hyperplane Arrangements

We mainly consider the topological and combinatorial properties of arrangements. This thesis consists of two parts: the characteristic polynomials of a class of the mixed arrangements and computation of the Orlik-Solomon algebras and their cohomologies for the real line arrangements.In the first part, the lattice properties of a mixed arrangement A| consisting of hyperplanes and spheres in R^l have been postulated and proved. The Mobius functionμ_A|- of the mixed arrangement was subsequently derived.A class of mixed arrangements with more than one spheres was studied and, finally, the characteristic polynomials and the formulae about the number of chambers were obtained.In the second part, we consider the computation of Orlik-Solomon algebras and their cohomologies for the real arrangements with up to 6 lines in affine plane and, finally, obtained some nice examples with special properties. For example, we obtained some arrangements with up to 6 lines in affine plane which areπ-equivalent and OS -equivalent but not (?)-equivalent.