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Conner Floyd

In the theory of spectra and generalized (co)homology theory in mathematics, the Conner–Floyd orientations (short CF orientations) are special spectrum morphisms. One is

MU
→
KU

{\displaystyle \operatorname {MU} \rightarrow \operatorname {KU} }

from the unitary Thom spectrum into complex/unitary K-theory, hence a complex orientation of

KU

{\displaystyle \operatorname {KU} }

, and the other is

MSU
→
KO

{\displaystyle \operatorname {MSU} \rightarrow \operatorname {KO} }

from the special unitary Thom spectrum into real/orthogonal K-theory. The CF orientations are named after Pierre Conner and Edwin Floyd, who described it in 1966. It laid the basics for the later generalization by the Landweber exact functor theorem.