On the \gamma-filtration of oriented cohomology of complete spin-flags

TL;DR

This paper investigates the gamma-filtration in algebraic oriented cohomology of complete spin-flags, providing new insights into torsion elements and conditions for torsion-freeness at low degrees.

Contribution

It introduces an annihilator for the torsion part of the gamma-filtration and identifies conditions under which the filtration is torsion free at degrees 2 and 3.

Findings

Annihilator of torsion in gamma-filtration established.

Gamma-filtration is torsion free at degrees 2 and 3 under certain conditions.

Provides structural understanding of cohomology of complete spin-flags.

Abstract

We study the characteristic map of algebraic oriented cohomology of complete spin-flags and the ideal of invariants of formal group algebra. As an application, we provide an annihilator of the torsion part of the $\gamma$-filtration. Moreover, if the formal group law determined by the oriented cohomology is congruent to the additive formal group law modulo 2, then at degree 2 and 3, the $\gamma$-filtration of complete spin-flags is torsion free.