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added a handful of further references to Witten genus, with brief comments.
Also ended up splitting off a stub for sigma-orientation.
I wonder if that’s a little confusing to begin
An elliptic genus or Witten genus is…
It make me think these are two names for exactly the same thing.
Right, thanks, I have changed that now.
Eventually that Idea-section needs to be refined further anyway. I’ll see if I find the time…
I have tried to bring the Idea-section at Witten genus into better shape.
I think it’s better now than it was, but it is not really good yet. Hope to come back to it.
I have expanded a bit more, and added more citations. In particular I hope I fixed the conditions for the various flavors of modularity now (rational/integral, congruence subgroup/full modular group).
just in case you are watching the logs and are wondering: I have added a few more pointers to and brief comments on Kefeng Liu’s work and generally a bunch of further pointers and brief comments to the literature in related entries.
Have added more on Witten genus – Characteristic series – In terms of Kac-Weyl characters.
This uses, under the hood, some standard relations between the splitting principle and the expression of Chern-characters in terms of maximal tori. I suppose one of the few places where this is actually explained well is
I’ll try to write something useful at splitting principle…
The subsection Integrality and modularity I have split in two pieces, one for the type II superstring (universal Ochanine elliptic genus) the other for the heterotic string (the Witten genus proper). Previously the two cases had been incorrectly mixed in that paragraph.
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