Related papers: Almost-Fuchsian representations in PU(2,1)

We develop the theory of maximal representations of the fundamental group of a compact connected oriented surface with boundary, into a group of Hermitian type. For any such representation we define the Toledo invariant, for which we…

Considering an integer $d>0$, we show the existence of convex-cocompactrepresentations of surface groups into SO(4,1) admitting an embedded minimal map withcurvatures in $(-1,1)$ and whose associated hyperbolic 4-manifolds are disk bundles…

We prove that the Fibonacci quantum representations $\rho_{g,n}:\rm{Mod}_{g,n}\to \rm{PU}(p,q)$ for $(g,n)\in\{(0,4),(0,5),(1,2),(1,3),(2,1)\}$ are holonomy representations of complex hyperbolic structures on some compactifications of the…

Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations,…

We study representations of lattices of PU(m,1) into PU(n,1). We show that if a representation is reductive and if m is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic m-space to complex…

This paper gives a construction for all minimal immersions $f$ of the Poincar\'{e} disc into the complex hyperbolic plane $\mathbb{CH}^2$ which are equivariant with respect to an irreducible representation $\rho$ of a hyperbolic surface…

We prove that any Borel Anosov representations of a surface group into $Sp(4,\mathbb{R})$ that has maximal Toledo invariant must be Hitchin. We also prove that a representation of a surface group into $Sp(2n,\mathbb{R})$ that is…

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called…

We develop Fenchel-Nielsen coordinates for representations of surface groups into Sp(2n,R) with maximal Toledo invariant. Analogous to classical Fenchel-Nielsen coordinates on the Teichm\"uller space they consist of a parametrization of…

In this paper, we address the issue of quaternionic Toledo invariant to study the character variety of two dimensional complex hyperbolic uniform lattices into $SU(n,2)$. We construct four distinct representations to prove that the…

We show the set of faithful representations of a closed orientable hyperbolic surface group is dense in both irreducible components of the PSL(2,K) representation variety, where K is the field of real or complex numbers, answering a…

We propose a definition of the Toledo invariant for representations of fundamental groups of smooth varieties of general type into semisimple Lie groups of Hermitian type. This definition allows to generalize the results known in the…

We give the quasi--Euclidean classification of the maximal (with respect to the $f$--vector) alcoved polyhedra. The $f$--vector of these maximal convex bodies is $(20,30,12)$, so they are simple dodecahedra. We find eight quasi--Euclidean…

We prove that convex-cocompact representations of finitely generated groups in the group of isometries of the infinite-dimensional hyperbolic space form an open set in the space of representations, allowing us to deform these…

For a compact Riemann surface $X$ of genus $g > 1$, $\Hom(\pi_1(X), PU(p,q))/PU(p,q)$ is the moduli space of flat $PU(p,q)$-connections on $X$. There are two invariants, the Chern class $c$ and the Toledo invariant $\tau$ associated with…

This paper deals with non-Archimedean representations of punctured surface groups in PGL(3), associated actions on Euclidean buildings (of type A2), and degenerations of real convex projective structures on surfaces. The main result is…

Using the L^2 norm of the Higgs field as a Morse function, we study the moduli spaces of U(p,q)-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on (p,q). A key step is…

We generalize the definition of the Toledo invariant for representations of fundamental groups of smooth varieties of general type due to Koziarz and Maubon to the context of singular klt varieties, where the natural fundamental groups to…

To each connected component in the space of semisimple representations from the orbifold fundamental group of the base orbifold of a Seifert fibered homology 3-sphere into the Lie group U(2,1), we associate a real number called the…

The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal…