A vanishing theorem for the homology of discrete subgroups of Sp(n, 1) and F-4(-20)

作者：Connell Chris^*; Farb Benson; McReynolds D B

来源：Journal of the London Mathematical Society-Second Series, 2016, 94(2): 357-376.

DOI：10.1112/jlms/jdw036

For any discrete, torsion-free subgroup G of Sp(n, 1) (respectively, F-4(-20)) with no parabolic elements, we prove that H4n-1(Gamma; V) = 0 (respectively, H-i(Gamma; V) = 0 for i = 13, 14, 15) for any Gamma-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 G, improving on the work of M. Kapovich.

• 出版日期2016-10