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- W1648260901 abstract "Let $bold G$ be a reductive algebraic group defined over $Q$, and let $Gamma$ be an arithmetic subgroup of $bold G(Q)$. Let $X$ be the symmetric space for $bold G(R)$, and assume $X$ is contractible. Then the cohomology (mod torsion) of the space $X/Gamma$ is the same as the cohomology of $Gamma$. In turn, $X/Gamma$ will have the same cohomology as $W/Gamma$, if $W$ is a ``spine'' in $X$. This means that $W$ (if it exists) is a deformation retract of $X$ by a $Gamma$-equivariant deformation retraction, that $W/Gamma$ is compact, and that $dim W$ equals the virtual cohomological dimension (vcd) of $Gamma$. Then $W$ can be given the structure of a cell complex on which $Gamma$ acts cellularly, and the cohomology of $W/Gamma$ can be found combinatorially." @default.
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- W1648260901 date "1997-12-15" @default.
- W1648260901 modified "2023-09-30" @default.
- W1648260901 title "Cohomology at infinity and the well-rounded retract for general linear groups" @default.
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- W1648260901 doi "https://doi.org/10.1215/s0012-7094-97-09015-3" @default.
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