Cobordism of flag bundles

Abstract

Let $G$ be a connected linear algebraic group over a field $k$ of characteristic zero. For a principal $G$-bundle $\pi :E\to X$ over a scheme $X$ of finite type over $k$ and a parabolic subgroup $P$ of $G$, we describe the rational algebraic cobordism and higher Chow groups of the flag bundle $E/P\to X$ in terms of the cobordism of $X$ and that of the classifying space of a maximal torus of $G$ contained in $P$. As a consequence, we also obtain the formula for the cobordism and higher Chow groups of the principal bundles over the scheme $X$. If $X$ is smooth, this describes the cobordism ring of these bundles in terms of the cobordism ring of $X$.

References in corpus (3)

• Algebraic cobordism
• Algebraic Cobordism of Classifying Spaces
• Riemann-Roch For Equivariant K-Theory

Cited by in corpus (1)

• Cobordism ring of toric varieties