Critical exponents for normal subgroups

Jeudi 29 mars 2018 14:00-15:00 - Rhiannon Dougall - Université de Nantes

Résumé : Fix a cocompact group 𝚪_0 of isometries of a negatively curved, simply connected space X. We are interested in the dynamics of its normal subgroups 𝚪. Namely, we study the critical exponent 𝛅(𝚪), which is the exponential growth rate of the 𝚪-orbit of a point. We characterise the existence of a gap 𝛅(𝚪) < 𝛅(𝚪_0) uniform in a family of normal subgroups 𝚪, in terms of permutation representations given by the quotients 𝚪_0/𝚪.
The proof uses the symbolic dynamics for the geodesic flow, for which we obtain the analogous statements for countable state shifts obtained as group extensions of a finite state shift.

Lieu : Institut de Mathématique d’Orsay, salle 2L8

Notes de dernières minutes : Café culturel à 13h par Damien Thomine.

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