A vanishing theorem for the homology of discrete subgroups of Sp(n, 1) and F4-20
نویسندگان
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.
منابع مشابه
A vanishing theorem for the homology of discrete subgroups
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 d...
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عنوان ژورنال:
- J. London Math. Society
دوره 94 شماره
صفحات -
تاریخ انتشار 2016