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In the paper (Osaka J. Math. {bf 46}: 403-409, 2009), Yang conjectured that a non-elementary subgroup $G$ of $SL(2, bc)$ containing elliptic elements is discrete if for each elliptic element $gin G$ the group $< f, g >$ is discrete, where $fin SL(2,bc)$ is a test map which is loxodromic or elliptic. The purpose of this paper is to give an affirmative answer to this question.
For every integer $g ,geq, 2$ we show the existence of a compact Riemann surface $Sigma$ of genus $g$ such that the rank two trivial holomorphic vector bundle ${mathcal O}^{oplus 2}_{Sigma}$ admits holomorphic connections with $text{SL}(2,{mathbb R})
We continue our study of genus 2 curves $C$ that admit a cover $ C to E$ to a genus 1 curve $E$ of prime degree $n$. These curves $C$ form an irreducible 2-dimensional subvariety $L_n$ of the moduli space $M_2$ of genus 2 curves. Here we study the ca
Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $varphi^* E$ is trivial for some surjective holomorphic map $varphi$, to $M$, from some compact complex manifold. We prove that these are exactly
We compute the Hodge-Deligne polynomials of the moduli spaces of representations of the fundamental group of a complex surface into SL(2,C), for the case of small genus g, and allowing the holonomy around a fixed point to be any matrix of SL(2,C), th
The crystalline period map is a tool for linearizing $p$-divisible groups. It has been applied to study the Langlands correspondences, and has possible applications to the homotopy groups of spheres. The original construction of the period map is inh