ترغب بنشر مسار تعليمي؟ اضغط هنا

On Benjamini--Schramm limits of congruence subgroups

71   0   0.0 ( 0 )
 نشر من قبل Arie Levit
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Arie Levit




اسأل ChatGPT حول البحث

Every sequence of orbifolds corresponding to pairwise non-conjugate congruence lattices in a higher rank semisimple group over local fields of zero characteristic is Benjamini--Schramm convergent to the universal cover.

قيم البحث

اقرأ أيضاً

We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces.
We prove that a uniform pro-p group with no nonabelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche-Wendt groups.
Let $A$ be the ring of elements in an algebraic function field $K$ over a finite field $F_q$ which are integral outside a fixed place $infty$. In an earlier paper we have shown that the Drinfeld modular group $G=GL_2(A)$ has automorphisms which map c ongruence subgroups to non-congruence subgroups. Here we prove the existence of (uncountably many) normal genuine non-congruence subgroups, defined to be those which remain non-congruence under the action of every automorphism of $G$. In addition, for all but finitely many cases we evaluate $ngncs(G)$, the smallest index of a normal genuine non-congruence subgroup of $G$, and compare it to the minimal index of an arbitrary normal non-congruence subgroup.
We classify the ergodic invariant random subgroups of block-diagonal limits of symmetric groups in the cases when the groups are simple and the associated dimension groups have finite dimensional state spaces. These block-diagonal limits arise as the transformation groups (full groups) of Bratteli diagrams that preserve the cofinality of infinite paths in the diagram. Given a simple full group $G$ admitting only a finite number of ergodic measures on the path-space $X$ of the associated Bratteli digram, we prove that every non-Dirac ergodic invariant random subgroup of $G$ arises as the stabilizer distribution of the diagonal action on $X^n$ for some $ngeq 1$. As a corollary, we establish that every group character $chi$ of $G$ has the form $chi(g) = Prob(gin K)$, where $K$ is a conjugation-invariant random subgroup of $G$.
We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the level and eigenvalue aspects of the theory. As a result, we present a ma thematically precise formulation of Berrys conjecture for a compact negatively curved manifold and formulate a Berry-type conjecture for sequences of locally symmetric spaces. We prove some we
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا