相关论文: Modular circle quotients and PL limit sets

F. Paulin proved that if the Gromov boundaries of two hyperbolic groups are quasi-Mobius equivalent, then the groups themselves are quasi-isometric. The goal of this article is to extend Paulin's result to the setting of relatively…

This paper is a more succinct version of the author's 1993 UCLA mathematics thesis. It proves that any group quasi-isometric to the product of the hyperbolic plane with the real line is a finite extension of a cocompact lattice in either…

Let $W$ be a Coxeter group whose proper parabolic subgroups are finite. According to Theorem~1.12 of [1], if the module of a finite $W$-digraph $\Gamma$ is isomorphic to the module of a $W$-graph over $Q$, then $\Gamma$ is acyclic. We…

We introduce a compact moduli scheme of marked noncommutative cubic surfaces as the GIT moduli scheme of relations of a quiver associated with a full strong exceptional collection on a cubic surface. It is a toric variety containing the…

Let $M$ be a finitely generated module over a Noetherian local ring. This paper gives, for a given parameter ideal $Q$ for $M$, bounds for the second Hilbert coefficients ${\mathrm{e}}_Q^2(M)$ in terms of the homological degrees and…

We construct cross sections for the geodesic flow on the orbifolds $\Gamma\backslash H$ which are tailor-made for the requirements of transfer operator approaches to Maass cusp forms and Selberg zeta functions. Here, $H$ denotes the…

The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…

Let M be an orientable hyperbolic surface without boundary and let $\gamma$ be a closed geodesic in M. We prove that any side of any triangle formed by distinct lifts of $\gamma$ in H2 is shorter than $\gamma$.

Recently, Morier-Genoud and Ovsienko introduced the $q$-deformed modular group. For construction, they first gave a group $G_q \subset \operatorname{GL}(2, {\mathbb Z}[q^{\pm}])$ and then set $\operatorname{PSL}_q(2,{\mathbb…

We describe the additive structure of the graded ring $\widetilde{M}_*$ of quasimodular forms over any discrete and cocompact group $\Gamma \subset \rm{PSL}(2, \RM).$ We show that this ring is never finitely generated. We calculate the…

The observation that the 0-dimensional Geometric Invariant $\Sigma ^{0}(G;A)$ of Bieri-Neumann-Strebel-Renz can be interpreted as a horospherical limit set opens a direct trail from Poincar\'e's limit set $\Lambda (\Gamma)$ of a discrete…

Let $\mathcal{S}$ be a surface of revolution embedded in the Heisenberg group $\mathcal{H}$. A revolution ring $R_{a,b}(\mathcal{S})$, $0<a<b$, is a domain in $\mathcal{H}$ bounded by two dilated images of $\mathcal{S}$, with dilation…

Let H be a discrete cocompact subgroup of SL_2(C). We conjecture that the quotient manifold X=SL_2(C)/H contains infinitely many non-isogeneous elliptic curves and prove that this is indeed the case if Schanuel's conjecture holds. We also…

Let $\Gamma$ be an $\widetilde A_2$ subgroup of $\PGL_3(\mathbb K)$, where $\mathbb K$ is a local field with residue field of order $q$. The module of coinvariants $C(\mathbb P^2_{\mathbb K},\mathbb Z)_{\Gamma}$ is shown to be finite, where…

We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable,…

We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l>2 be prime and A a finite abelian l-group. Then there…

Let $\calM=\Gamma\bs \calH^{(n)}$, where $\calH^{(n)}$ is a product of $n+1$ hyperbolic planes and $\Gamma\subset\PSL(2,\bbR)^{n+1}$ is an irreducible cocompact lattice. We consider closed geodesics on $\calM$ that propagate locally only in…

A hyperbolic polygon is defined to be cyclic, horocyclic, or equidistant if its vertices lie on a metric circle, horocycle, or a component of the equidistant locus to a hyperbolic geodesic, respectively. Convex such $n$-gons are…

We consider a class of Hamiltonians in $L^2(\R^2)$ with attractive interaction supported by piecewise $C^2$ smooth loops $\Gamma$ of a fixed length $L$, formally given by $-\Delta-\alpha\delta(x-\Gamma)$ with $\alpha>0$. It is shown that…

Let $\Gamma$ be a torsion-free hyperbolic group. We study $\Gamma$--limit groups which, unlike the fundamental case in which $\Gamma$ is free, may not be finitely presentable or geometrically tractable. We define model $\Gamma$--limit…