TY - JOUR
T1 - Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance
AU - Dougall, Rhiannon
PY - 2019/6/20
Y1 - 2019/6/20
N2 -
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.
AB -
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.
KW - Critical exponent
KW - Kazhdan
KW - Negatively curved space
KW - Transfer operator
UR - http://www.scopus.com/inward/record.url?scp=85064312013&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2019.04.016
DO - 10.1016/j.aim.2019.04.016
M3 - Article (Academic Journal)
AN - SCOPUS:85064312013
SN - 0001-8708
VL - 349
SP - 316
EP - 347
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -