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.

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.