Homological algebra/Group theory
A refinement of a conjecture of Quillen
Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 779-784.

We present some new results on the cohomology of a large scope of SL2 groups in degrees above the virtual cohomological dimension, yielding some partial positive results for the Quillen conjecture in rank one. We combine these results with the known partial positive results and the known types of counterexamples to the Quillen conjecture, in order to formulate a refined variant of the conjecture.

Nous présentons de nouveaux résultats sur la cohomologie d'un grand échantillon de groupes SL2, en degrés au-dessus de la dimension cohomologique virtuelle. Ceci donne quelques résultats affirmatifs de caractère partiel pour la conjecture de Quillen en rang 1. Nous combinons ces résultats avec les résultats connus affirmant une partie de la conjecture de Quillen et avec les types connus de contre-exemples à cette conjecture, afin de formuler une variante raffinée de cette dernière.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.03.022
Rahm, Alexander D. 1; Wendt, Matthias 2

1 Department of Mathematics, National University of Ireland at Galway, Ireland
2 Fakultät Mathematik, Universität Duisburg-Essen, Thea-Leymann-Strasse 9, Essen, Germany
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Rahm, Alexander D.; Wendt, Matthias. A refinement of a conjecture of Quillen. Comptes Rendus. Mathématique, Volume 353 (2015) no. 9, pp. 779-784. doi : 10.1016/j.crma.2015.03.022. http://www.numdam.org/articles/10.1016/j.crma.2015.03.022/

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