The two maps on top are analytic and topological shriek maps.
If you mix up which of the analytic or topological maps you do, you get the index theorem in all it's forms.
Replace K theory with TMF and the A-hat with the Witten genus should give you a beefed up version.
I don't know which of the maps have been constructed, but this is where a punt to Stolz-Teichner and crew goes.
The idea is we know the Spectra which represent K theory in all it's flavors, BU and all that. If that TMF is also a generalized cohomology theory, what is it's spectrum. Insert the suspected one here.
credit talks given by Dan Berwick-Evans
I don't know which of the maps have been constructed, but this is where a punt to Stolz-Teichner and crew goes.
The idea is we know the Spectra which represent K theory in all it's flavors, BU and all that. If that TMF is also a generalized cohomology theory, what is it's spectrum. Insert the suspected one here.
credit talks given by Dan Berwick-Evans
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