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

Research output: Contribution to journalArticle (Academic Journal)

2 Citations (Scopus)
38 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)316-347
Number of pages32
JournalAdvances in Mathematics
Volume349
Early online date17 Apr 2019
DOIs
Publication statusPublished - 20 Jun 2019

Keywords

  • Critical exponent
  • Kazhdan
  • Negatively curved space
  • Transfer operator

Fingerprint Dive into the research topics of 'Critical exponents of normal subgroups, the spectrum of group extended transfer operators, and Kazhdan distance'. Together they form a unique fingerprint.

  • Cite this