Buhstaber's work on two-valued formal groups

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The paper which follows may be regarded as the best substitute available for the lecture which V.M. Buhstaber would have delivered to the International Congress of Mathematicians, Vancouver 1974, if he had been present. (We would like to say how sorry we are that he was not able to be there.) In fact, we originally agreed to prepare it for submission to the Proceedings of the Congress. The text is in the form of a report on Buhstaber's work by J.F. Adams and A. Liulevicius, and these two authors accept entire responsibility for it. Of course, our primary source is the account of Buhstaber's work which we heard at the Congress from A.T. Fomenko, and we would like to thank him for all his help. But we have also tried to improve our understanding by consulting the papers which Buhstaber has published in Russian. We assume that the reader is aware of the connection between complex cobordism and the theory of formal groups [2, 5]; this work is generally respected. The topic of two-valued formal groups represents an extension of this theory. It is conceived partly as a contribution to pure algebra, but it is inspired by an application to algebraic topology; this application lies in the theory of characteristic classes of symplectic bundles, and in the study of symplectic cobordism.