Abstract
In [38] Thom defined the unoriented and oriented cobordism rings, soon generalized to complex cobordism by Milnor [19] and Novikov [22]. These geometric constructions were later shown to give rise to generalized homology and cohomology theories [39] by Atiyah [3]. These theories have received a great deal of attention in recent years. In this paper we offer three new things. First, we obtain unstable homotopy theoretic information from formal group laws. Second, we make essential use of the concept of Hopf rings both in the description of our results and in the proofs. Third, we give a detailed analysis of the homology structure of the (unstable) classifying spaces for complex cobordism, including a completely algebraic construction which contains total information about the unstable complex cobordism operations. Some of our results were announced in [29].
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