Darondeau-Pragacz formulas in complex cobordism
Masaki Nakagawa, Hiroshi Naruse
TL;DR
This paper extends Darondeau-Pragacz formulas to complex cobordism, introduces universal quadratic Schur functions, and derives new Gysin formulas, broadening the theoretical framework for flag bundle computations.
Contribution
It generalizes push-forward formulas to complex cobordism and introduces universal quadratic Schur functions with associated Gysin formulas.
Findings
Generalized Darondeau-Pragacz formulas to complex cobordism
Defined universal quadratic Schur functions
Established Gysin formulas for these functions
Abstract
In this paper, we generalize the push-forward (Gysin) formulas for flag bundles in the ordinary cohomology theory, which are due to Darondeau-Pragacz, to the complex cobordism theory. Then we introduce the {\it universal quadratic Schur functions}, which are a generalization of the (ordinary) quadratic Schur functions introduced by Darondeau-Pragacz, and establish some Gysin formulas for the universal quadratic Schur functions as an application of our Gysin formulas.
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