The Orlik-solomon Algebra And The Cohomology Group Of Single Coaxial Sphere Arrangement In 2-dimension Sphere

In this paper, the definition of a sphere arrangement is given and a kind of clas-sification method is obtained under the equivalence relation of "coaxality"in S2. The formulas to compute the characteristic polynomial and the number of regions of the special r coaxial sphere arrangement are given. And we study the single coaxial sphere arrangement in S2, get its Orlik-Solomon algebra and the dimension of its cohomology group. Then we obtain the Orlik-Solomon algebra of the generalized Shi arrangement in R3 from the NBC base.