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Publication - Dr Rhiannon Dougall

    Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance

    Citation

    Dougall, R, 2019, ‘Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance’. Advances in Mathematics, vol 349., pp. 316-347

    Abstract


    For a pinched Hadamard manifold X and a discrete group of isometries Γ of X, the critical exponent δ
    Γ
    is the exponential growth rate of the orbit of a point in X under the action of Γ. We show that the critical exponent for any family N of normal subgroups of Γ
    0
    has the same coarse behaviour as the Kazhdan distances for the right regular representations of the quotients Γ
    0
    /Γ. The key tool is to analyse the spectrum of transfer operators associated to subshifts of finite type, for which we obtain a result of independent interest.

    Full details in the University publications repository