Spin cobordism determines real K-theory (Q1204266)

The main result of this paper is that homomorphisms \(M\text{Spin}_ *(X)\otimes_{M\text{Spin}_ *}\text{KO}_ *\to \text{KO}_ *(X)\) and \(M\text{Spin}^ c_ *(X)\otimes_{M\text{Spin}_ *^ c}\text{K}_ *\to \text{K}_ *(X)\) are isomorphisms. These results are analogues of the Conner-Floyd theorem relating complex bordism and \(K\)-theory. Since the determination of Spin bordism by Anderson, Brown, and Peterson, everyone has known that these results were true. Unfortunately, that well-known truth was folklore unsupported by proof. A valid proof is difficult, and this paper finally justifies the result.