# Stability of Bott--Samelson Classes in Algebraic Cobordism

## TL;DR

This paper constructs and analyzes stable Bott--Samelson classes within algebraic cobordism, providing explicit formulas and computations, especially in infinitesimal cohomology, to understand their behavior across flag varieties.

## Contribution

It introduces stable Bott--Samelson classes in algebraic cobordism and derives explicit formulas for their restrictions, advancing the understanding of their structure and stability.

## Key findings

- Explicit power series representations of stable Bott--Samelson classes.
- Formulas for restrictions of classes to smaller flag varieties.
- Computations in the case of infinitesimal cohomology.

## Abstract

In this paper, we construct stable Bott--Samelson classes in the projective limit of the algebraic cobordism rings of full flag varieties, upon an initial choice of a reduced word in a given dimension. Each stable Bott--Samelson class is represented by a bounded formal power series modulo symmetric functions in positive degree. We make some explicit computations for those power series in the case of infinitesimal cohomology. We also obtain a formula of the restriction of Bott--Samelson classes to smaller flag varieties.

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Source: https://tomesphere.com/paper/1907.06024