The Bockstein Spectral Sequence for UM[sup(k)]

We continue our analysis of the dgH (UMk,d ) by computing its homology. Because of the quism B k —► UMk, we are simultaneously computing the homology of (J5*,d), i.e., the homology of the space ΩΖ)*. We first introduce a trick for converting facts about polynomials in one variable into relations among the elements of UMk. After gaining fluency in the use of this trick we establish several formulas that are valid in UMk, and we compute explicitly the BSS for UMk. The highlights of Chapter 4 are the innocent-looking formulas (4M), whose geometric counterparts will be pivotal, and the determination that UMk has exponent pr+*, i.e., pr+kH*(UMk, d) = 0.