Rational homology of the group \(\text{O}_n(\mathbb{Z}[\tfrac 12])\) and automorphisms of unimodular lattices (Q699220)
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scientific article; zbMATH DE number 1803914
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rational homology of the group \(\text{O}_n(\mathbb{Z}[\tfrac 12])\) and automorphisms of unimodular lattices |
scientific article; zbMATH DE number 1803914 |
Statements
Rational homology of the group \(\text{O}_n(\mathbb{Z}[\tfrac 12])\) and automorphisms of unimodular lattices (English)
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31 March 2003
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The dimension of the rational homology of the group \(\text{O}_n(\mathbb{Z}[1/2])\) in degree equal to the virtual cohomological dimension, for \(n\) large, is estimated. This provides an indication for the failure of a conjecture of Quillen about modulo 2 cohomology of \(\text{GL}_n(\mathbb{Z}[1/2])\).
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Quillen's conjecture
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rational homology
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virtual cohomological dimension
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