Forms of K-theory (Q921658)

This paper describes several interesting integral genera for complex manifolds which arise from number theoretic considerations. The integrality is generally nontrivial and derives from the theory of formal groups, the significance of which is due to Quillen's identification of complex bordism with the universal formal group. The formal groups also lead to associated homology theories, and most of the paper is concerned with a family of these homology theories which are seen as analogues of ordinary K-theory. This paper was written in 1973, but the author chose not to submit it for publication until recently pressed to do so. The study of elliptic genera and elliptic cohomology are based on very much the same ideas used in this paper and, indeed, this paper is a natural ancestor for the ideas of elliptic theory.