Vanishing conjecture for the top cohomology of SLnZ\operatorname{SL}_n\mathbb{Z}

Let SLnZ\operatorname{SL}_n\mathbb{Z} be the special linear group over the integers, and let H(;Q)H^*(-;\mathbb{Q}) denote rational group cohomology. Vanishing conjecture. H(n2)i(SLnZ;Q)=0H^{\binom{n}{2}-i}(\operatorname{SL}_n\mathbb{Z};\mathbb{Q})=0 for all i<n1i<n-1. This vanishing is presented as a consequence of the proposed stable instability and reflects torsion phenomena in the arithmetic group; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Thomas Church, Benson Farb and Andrew Putman, “A stability conjecture for the unstable cohomology of SL_n Z, mapping class groups, and Aut(F_n)”, arXiv:1208.3216 (2013).

Additional references

2 papers in this index state this conjecture (2010–2012). The statement above is taken from the most recent of them; the others are arXiv:1008.1368.

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