A vanishing theorem for the homology of discrete subgroups
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چکیده
For any discrete, torsion-free subgroup Γ of Sp(n, 1) (resp. F−20 4 ) with no parabolic elements, we prove that H4n−1(Γ;V ) = 0 (resp. Hi(Γ;V ) = 0 for i = 13, 14, 15) for any Γ–module V . The main technical advance is a new bound on the p–Jacobian of the barycenter map of Besson–Courtois–Gallot. We also apply this estimate to obtain an inequality between the critical exponent and homological dimension of Γ, improving on work of M. Kapovich.
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تاریخ انتشار 2015