Talk:Atiyah–Bott fixed-point theorem

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What vector bundles?

The article refers to vector bundles E_j as follows in the Formulation section:

"Further data needed relates to the elliptic complex of vector bundles E_j, namely a bundle map from

φ_j:f⁻¹ E_j → E_j

for each j, such that the resulting maps on sections give rise to an endomorphism of the elliptic complex T."

But nowhere is it stated which vector bundles are being discussed here, or what "elliptic complex" is being discussed.

Later in this Formulation section, it reads:

"Specializing the Atiyah–Bott theorem to the de Rham complex of smooth differential forms yields the original Lefschetz fixed-point formula."

But one cannot specialize something unless it has been stated first in more generality. I hope someone knowledgeable on this subject can fix this serious omission, so that the article might make sense.Daqu (talk) 17:51, 21 October 2016 (UTC)[reply]