Open Collections

Abstract

In this thesis, we study the cohomology ring of BPSO(8m+4) for all positive integers m≥1. Specifically, we will calculate the ring structure of H*(BPSO(8m+4))≤¹⁴. When m=1, we also figure out the H*(BPSO(8m+4))≤¹⁵. The basic tool is the Eilenberg-Moore spectral sequence. We write code to compute the elements of the E₂ page of the spectral sequence. By comparison with the sequence of H*(BPSO(6)) and H*(BPSO(4)), we show that the spectral sequence collapses up to degree 15 when m=1 and degree 14 when m>1.