arXiv subjects

Arie Levit

Publications and source records attributed to Arie Levit.

21 records · Page 2Linked to original sources

arXiv2017

Invariant random subgroups over non-Archimedean local fields

Let $G$ be a higher rank semisimple linear algebraic group over a non-Archimedean local field. The simplicial complexes corresponding to any sequence of pairwise non-conjugate irreducible lattices in $G$ are Benjamini-Schramm convergent to the Bruhat-Tits building. Convergence of the relative Plancherel measures and normalized Betti numbers follows. This extends the work of Abert, Bergeron, Biringer, Gelander, Nokolov, Raimbault and Samet from real Lie groups to linear groups over arbitrary local fields. Along the way, various results concerning Invariant Random Subgroups and in particular a variant of the classical Borel density theorem are also extended.

math.GR↗

arXiv2016

The Nevo-Zimmer intermediate factor theorem over local fields

The Nevo-Zimmer theorem classifies the possible intermediate $G$-factors $Y$ in $X \times G/P \to Y \to X$, where $G$ is a higher rank semisimple Lie group, $P$ a minimal parabolic and $X$ an irreducible $G$-space with an invariant probability measure. An important corollary is the Stuck-Zimmer theorem, which states that a faithful irreducible action of a higher rank Kazhdan semisimple Lie group with an invariant probability measure is either transitive or free, up to a null set. We present a different proof of the first theorem, that allows us to extend these two well-known theorems to linear groups over arbitrary local fields.

math.DS↗

arXiv2014

Counting commensurability classes of hyperbolic manifolds

Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v^v such manifolds of volume at most v, considered up to commensurability. Since the number of arithmetic ones tends to be polynomial, almost all hyperbolic manifolds are non-arithmetic in an appropriate sense. Our method involves a geometric graph-of-spaces construction that relies on arithmetic properties of certain quadratic forms.

math.GT↗