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Cobordism of flag bundles | | Amalendu Krishna
; | | Date: |
7 Jul 2010 | | Abstract: | Let $G$ be a connected linear algebraic group over a field $k$ of
characteristic zero. For a principal $G$-bundle $pi: E o X$ 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 $E/P
o X$ 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 $X$. | | Source: | arXiv, 1007.1083 | | Services: | Forum | Review | PDF | Favorites | |
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