Abstract
In algebraic topology, The Brown Peterson theory plays an important role. Unfortunately, there is not many results. In this paper, we try to compute the Brown Peterson homology of the infinite orthogonal group.The method we used in this paper is the Adams spectral sequence. The method is divided into three parts. The first part is to describe the Adams E2 term. The second part is to prove that the spectral sequence collapses at the E2 term. The third part is to solve the group extension problem.In this paper, we have completely described the Adams E2 term. We also proved that part of generators in the Adams E2 term are permanent cycles. Finally we gave a partial solution of the group extension problem.This paper is divided into two parts. The first part is to introduce the general background. That includes the general homology theory, the Brown Peterson theory and the Adams spectral sequence. The second part is to describe our work. That includes the description of the Adams E2 term, part of the generators in the Adams E2 are permanent cycles and the canonical generators in the Brown Peterson homology corresponding to the generators in the Adams E2.