Related papers: Totally elliptic surface group representations

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

In this paper we prove that every open Riemann surface properly embeds in the Special Linear group $SL_2(\mathbb{C})$ as a holomorphic Legendrian curve, where $SL_2(\mathbb{C})$ is endowed with its standard contact structure. As a…

For each closed orientable surface we introduce a simplical complex with some additional structure which is a version of the complex of curves of this surface adjusted to investigation of its Torelli group. We call this complex the Torelli…

The first part of this paper surveys several characterizations of Teichm\"uller space as a subset of the space of representation of the fundamental group of a surface into PSL(2,R). Special emphasis is put on (bounded) cohomological…

We consider algebraic surfaces, recently constructed by Schreieder, that are smooth models of the quotient of the self-product of a complex hyperelliptic curve by a $(\mathbb{Z}/3^c\mathbb{Z})$-action. We show that these surfaces are…

We characterize the representations of the fundamental group of a closed surface to $\mathrm{PSL}_2(\mathbb C)$ that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the…

Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…

For each prime number $\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order…

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an `evolution operator' exists). Up to now all known smooth Lie groups…

We construct orbits of the absolute Galois group, of explicit unbounded size, consisting of surfaces with mutually non-isomorphic fundamental groups. These are Beauville surfaces with Beauville group PGL_2(p).

We study real elliptic surfaces and trigonal curves (over a base of an arbitrary genus) and their equivariant deformations. We calculate the real Tate-Shafarevich group and reduce the deformation classification to the combinatorics of a…

Let $C$ be a smooth projective curve defined over $\Qbar$, let $\pi:\mathcal{E}\lra C$ be an elliptic surface and let $\sigma_{P_1},\sigma_{P_2},\sigma_{Q}$ be sections of $\pi$ (corresponding to points $P_1,P_2, Q$ of the generic fiber $E$…

For any finite type connected surface $S$, we give an infinite presentation of the fundamental group $\pi_1(S,\ast)$ of $S$ based at an interior point $\ast\in{S}$ whose generators are represented by simple loops. When $S$ is…

We show that every connected real Lie group can be realized as the full automorphism group of a Stein hyperbolic complex manifold.

The structure of the Tate-Shafarevich groups of a class of elliptic curves over global function fields is determined. These are known to be finite abelian groups from the monograph [1] and hence they are direct sums of finite cyclic groups…

We fill in the details in a procedure outlined by Serre for drawing pictures of compact real Lie groups. In the case of Sp($2n$), the picture generated by the method is connected with abelian varieties over a number field or a finite field.…

The multidimensional quantization procedure, proposed by the first author and its modifications (reduction to radicals and lifting on U(1)-coverings) give us a almost universal theoretical tools to find irreducible representations of Lie…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We study the question of whether the topological quotient of a real linear representation of a simple three-dimensional compact Lie group is a manifold. We obtain an upper bound for the dimension of a representation whose quotient is a…

For each finite primitive subgroup $G$ of $\operatorname{PGL}_4(\mathbb{C})$, we find all the smooth $G$-invariant quartic surfaces. We also find all the faithful representations in $\operatorname{PGL}_4(\mathbb{C})$ of the smooth quartic…