nLab
string orientation of tmf

Idea

A refinement of the Witten genus to a morphism of E-infinity rings

$$M\mathrm{String}\to \mathrm{tmf}$$M String \to tmf

from the String structure-Thom spectrum to tmf: an orientation in generalized cohomology.

References

• Matthew Ando, Mike Hopkins, Charles Rezk, Multiplicative orientations of KO-theory and the spectrum of topological modular forms (pdf)