Universal Gysin formulas for flag bundles
Lionel Darondeau, Piotr Pragacz
TL;DR
This paper derives universal push-forward formulas for all types of flag bundles, enabling simplified calculations using Segre and characteristic classes, and introduces new determinantal formulas as applications.
Contribution
It provides the first comprehensive push-forward formulas for all flag bundle types, utilizing only Segre and universal bundle classes, with new determinantal formulas as applications.
Findings
Unified push-forward formulas for all flag bundle types.
Formulas involve only Segre classes and universal bundle characteristic classes.
New determinantal formulas derived as applications.
Abstract
We give push-forward formulas for all flag bundles of types A, B, C, D. The formulas (and also the proofs) involve only Segre classes of the original vector bundles and characteristic classes of universal bundles. As an application, we provide new determinantal formulas.
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