FQFT and cohomology
See there for background and context.
As described at (2,1)-dimensional Euclidean field theories and tmf, the idea is that (2,1)-dimensional Euclidean field theories are a geometric model for tmf cohomology theory.
While there is no complete proof of this so far, here we discuss the construction and proof – due to Stephan Stolz and Peter Teichner – for the situation over the point: the partition function of a -dimensional EFT is a modular form. Hence -dimensional EFTs do yield the correct cohomology ring of tmf over the point.