Thom-Porteous formulas in algebraic cobordism

TL;DR

This paper derives a formula for push-forward classes in algebraic cobordism related to Bott-Samelson resolutions and connects it to double beta-polynomials through K-theory specialization.

Contribution

It introduces a new formula for push-forward classes in algebraic cobordism and offers a geometric interpretation of double beta-polynomials.

Findings

Derived a push-forward class formula in algebraic cobordism

Connected the formula to double beta-polynomials via K-theory

Provided geometric insights into algebraic cobordism computations

Abstract

We prove a formula for the push-forward class of Bott-Samelson resolutions in the algebraic cobordism ring of the flag bundle. We then provide a geometric interpretation to the double beta-polynomials of Fomin and Kirillov by specializing our formula to the case of connected K-theory.