Related papers: Surface group representations to $SL(2,{\mathbb C}…

We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and…

In math.SG/0303255, we discussed the connected components of the space of surface group representations for any compact connected semisimple Lie group and any closed compact (orientable or nonorientable) surface. In this sequel, we…

In this paper we determine the spectral data parametrizing Higgs bundles in a generic fiber of the Hitchin map for the case where the structure group is the special Clifford group with fixed Clifford norm. These are spin and "twisted" spin…

Let G be a connected, compact, semisimple Lie group. It is known that for a compact closed orientable surface $\Sigma$ of genus $l >1$, the order of the group $H^2(\Sigma,\pi_1(G))$ is equal to the number of connected components of the…

We characterize those unipotent representations of the fundamental group $\pi_1(X,x)$ of a compact Kaehler manifold $X$, which correspond to a Higgs bundle whose underlying Higgs field is equal to zero. The characterization is parallel to…

We introduce and study (strict) Schottky G-bundles over a compact Riemann surface X, where G is a connected reductive algebraic group. Strict Schottky representations are shown to be related to branes in the moduli space of G-Higgs bundles…

Let $G$ be a split real form of a complex simple adjoint group whose Weyl group contains $-1$, let $\lambda$ be the Jordan projection of $G$, and let $S$ be a closed orientable surface of genus at least 2. For a $G$-Hitchin representation…

Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not…

Let $k$ be an algebraic closure of a finite field of odd characteristic. We prove that for any rank two graded Higgs bundle with maximal Higgs field over a generic hyperbolic curve $X_1$ defined over $k$, there exists a lifting $X$ of the…

We carry an intrinsic approach to the study of the connectedness of the moduli space $\mathcal{M}_G$ of $G$-Higgs bundles, over a compact Riemann surface, when $G$ is a complex reductive (not necessarily connected) Lie group. We prove that…

We extend the notion of Hitchin component from surface groups to orbifold groups and prove that this gives new examples of higher Teichm\"{u}ller spaces. We show that the Hitchin component of an orbifold group is homeomorphic to an open…

We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1. Following [1], we construct a projective unitary representation of pi_1(Sigma) realized on L^2(H), with H the upper half-plane. As a first step we introduce a suitably…

We study a natural map from representations of a free group of rank g in GL(n,C), to holomorphic vector bundles of degree 0 over a compact Riemann surface X of genus g, associated with a Schottky uniformization of X. Maximally unstable flat…

We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact K\"ahler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of…

Let $S$ be a Riemann surface obtained by deleting a finite number of points, called cusps, from a compact Riemann surface. Let $\rho: \pi_1(S)\to Sl(n, \mathbb{C})$ be a semisimple linear representation of $\pi_1(S)$ which is unipotent near…

Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find…

We will construct a non-separable Hilbert space for which the inhomogeneous ${\rm SL}(2,\mathbb{C})$ acts on it unitarily. Each vector in this Hilbert space is described by a (rectangular) space-like surface in $\mathbb{R}^4$, for which a…

In very rough terms, the main theorem is that the set, which consists of semistable vector bundles with trivial rational Chern classes and nontrivial kth cohomology on a smooth complex projective variety, is a degeneration of a union of…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham…