On a question of Serre - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2012

On a question of Serre

Alexander D. Rahm

Résumé

Consider the Borel-Serre compactification of the quotient of hyperbolic 3-space $\Hy$ by a finite index subgroup $\Gamma$ in a Bianchi group, and in particular the following question which Serre poses on page 514 of the quoted article. Consider the map~$\alpha$ induced on homology when attaching the boundary into the Borel-Serre compactification. How can one determine the kernel of $\alpha$ (in degree 1) ? Serre uses a global topological argument and obtains the rank of the kernel of $\alpha$. But in the quoted article, he kept asking what submodule precisely this kernel is. With a local topological study, we can decompose the kernel of $\alpha$ into its parts associated to each cusp.
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Dates et versions

hal-00670217 , version 1 (14-02-2012)
hal-00670217 , version 2 (12-07-2012)
hal-00670217 , version 3 (20-07-2012)
hal-00670217 , version 4 (05-09-2012)

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Alexander D. Rahm. On a question of Serre. 2012. ⟨hal-00670217v2⟩
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