Geodesic
The Farrell cohomology of ${Sp}(p-1,\bbfZ)$
Documenta mathematica, Tome 7 (2002), pp. 239-254.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $p$ be an odd prime with odd relative class number $h^-$. In this article we compute the Farrell cohomology of $\mathrm{Sp}(p-1,\mathbb Z)$, the first $p$-rank one case. This allows us to determine the $p$-period of the Farrell cohomology of $\mathrm{Sp}(p-1,\mathbb Z)$, which is $2y$, where $p-1=2^r y, y$ odd. The $p$-primary part of the Farrell cohomology of $\mathrm{Sp}(p-1,\mathbb Z)$ is given by the Farrell cohomology of the normalizers of the subgroups of order $p$ in $\mathrm{Sp}(p-1,\mathbb Z)$. We use the fact that for odd primes $p$ with $h^-$ odd a relation exists between representations of $\mathbb Z/p\mathbb Z$ in $\mathrm{Sp}(p-1,\mathbb Z)$ and some representations of $\mathbb Z/p\mathbb Z$ in $\mathrm{U}((p-1)/2)$.
Classification : 20G10
Keywords: cohomology theory 
@article{DOCMA_2002__7__a8,
     author = {Busch, Cornelia},
     title = {The {Farrell} cohomology of ${Sp}(p-1,\bbfZ)$},
     journal = {Documenta mathematica},
     pages = {239--254},
     publisher = {mathdoc},
     volume = {7},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a8/}
}
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Busch, Cornelia. The Farrell cohomology of ${Sp}(p-1,\bbfZ)$. Documenta mathematica, Tome 7 (2002), pp. 239-254. http://geodesic.mathdoc.fr/item/DOCMA_2002__7__a8/