Formal groups, power systems and Adams operators

This paper provides a systematic presentation of the connection between the theory of one-dimensional formal groups and the theory of unitary cobordism. Two new algebraic concepts are introduced: formal power systems and two-valued formal groups. A presentation of the general theory of formal power systems is given, and it is shown that cobordism theory gives a nontrivial example of a system which is not a formal group. A two-valued formal group is constructed whose ring of coefficients is closely related to the bordism ring of a symplectic manifold. Finally, applications of formal groups and power systems are made to the theory of fixed points of periodic transformations of quasicomplex manifolds.
Bibliography: 17 titles.