Surface group representations. Google Scholar Goldman, W.

Surface group representations. Goldman Department of Mathematics University of Maryland Colloque de mathematiques de Montreal CRM/ISM Let $\Sigma_ {g,n}$ be an orientable surface of genus $g$ with $n$ punctures. , the fundamental group of a The space of Surface group representations. We require that the genus of Abstract and Figures We study a family of compact components of totally elliptic representations of the fundamental group of For any maximal surface group representation into $$\\textrm{SO}_0(2,n+1)$$ SO 0 ( 2 , n + 1 ) , we introduce a non-degenerate scalar product on the first cohomology group of In the context of Goldman's paper The symplectic nature of fundamental groups of surfaces: Consider a closed oriented surface $S$ with fundamental group $\\pi$, and . We emphasize the The surface group representations in real semisimple Lie groups with maximal Toledo invariant provide an interesting concrete example of such groups. We study actions of the mapping class group $\mathrm {Mod}_ {g,n}$ of $\Sigma _ {g,n}$ via The subject of these notes is the character variety of representations of a surface group in a Lie group. The We give an overview of the work of Corlette, Donaldson, Hitchin and Simpson leading to the non-abelian Hodge theory correspondence In this paper, we study the moduli space of representations of a surface group (that is, the fundamental group of a closed oriented surface) in the real symplectic group Sp (2n, ℝ). We emphasize the Abstract Let $\Sigma _ {g,n}$ be an orientable surface of genus $g$ with $n$ punctures. Surface Group Representations and U (p, q)-Higgs BundlesSurface group representations and U (p, q)-Higgs bundles are examined to elucidate their implications in mathematical physics. Finally weinterpret (using the moment-map We develop a complete Hitchin-Kobayashi correspondence for twisted pairs on a compact Riemann surface X. AG] 11 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. (with an We study representations of compact surface groups on Hermitian symmetric spaces and characterize those with maximal Toledo invariant. Goldman Published 1 June 1986 Invariant functions on Lie groups and Hamiltonian flows of surface group representations Published: June 1986 Volume 85, pages 263–302, (1986) Cite this article We describe the modifications needed to construct Liealgebras ased on curves which act on Hom(zt, G)/G for the other classical L groups e G. We show that every Let Σgbe a compact, connected, orientable surface of genusg≥ 2. We leave the proofs to the reader – all are direct consequences of Theorem 2. We show that every geometric representation of into the group of orientation-preserving homeomorphisms of Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. Invariant functions on Lie groups and Hamiltonian flows of surface group representations. I intend to study of the limit set of The relation between Higgs bundles and surface group representations has been successfully exploited by others, going back originally to the work of Hitchin and Simpson on complex We develop the theory of maximal representations of the fundamental group 7i\ (S) of a compact connected oriented surface ? (possibly with boundary) into Lie groups G of Hermitian type. Goldman, W. The Invariant functions on Lie groups and Hamiltonian flows of surface group representations William M. This article discusses the study of surface group Download Citation | On Dec 1, 2013, François Labourie published Lectures on Representations of Surface Groups | Find, read and cite all the research you need on ResearchGate Let \ (\rho \) be a representation of the fundamental group of a punctured surface into \ ( {\textrm {PSL}_2 (\mathbb {C})}\) that is not This relation between Higgs bundles and surface group representations has been successfully exploited by others, going back originally to the work of Hitchin and Simpson on complex PDF | Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group In this paper, by using Atiyah-Patodi-Singer index theorem, we obtain a formula for the signature of a flat symplectic vector bundle over a Introduction In the theory of surface group representations, understanding the topology of representation spaces is a fundamental topic which influenced many branches of mathematics Download Citation | Dominating Surface Group Representations by Fuchsian Ones | We prove that a representation from the fundamental group of a closed surface of negative This was used by Labourie [Lab17] to study Hitchin representations into PSL (3, R), PSp (4, R) and G 2 , by the first author [Col16b] to study some maximal representations in In this note we prove that the number of irreducible components of Hom (π,G) is the same as π1(G), where π is a surface group andG is complex semisimple. Google Scholar Goldman, W. These spaces admit natural actions of the Download Citation | Spaces of surface group representations | Let \ (\Gamma _g\) denote the fundamental group of a closed surface of genus \ (g \ge 2\). This article discusses the study of surface group Many are known on representations of surface group, and the story about surface groups is different from higher dimensional manifold groups, which we will eventually These notes were originally designed for students with only elementary knowledge of differential geometry and topology. In Section 1, we recall the definition of the signature for surface group representations into SL(2, R), along with the Toledo invariant, relative Euler class, and the rho invariant. Inventiones Mathematicae. 8 and basic properties of This article examines surface group representations, their properties, and geometric implications. For any Because of the relation between flat bundles and fundamental group representations, we can interpret our conclusions as results about the number of connected components in the moduli Because of the relation between flat bundles and fundamental group representations, we can interpret our conclusions as results about the number of connected components in the moduli Because of the relation between flat bundles and fundamental group representations, we can interpret our conclusions as results about the number of connected Recently Deroin, Tholozan and Toulisse found connected components of relative character varieties of surface group representations in a Hermitian Lie group G G with The subject of these notes is the character variety of representations of a surface group in a Lie group. Given an oriented surface of positive genus with nitely many punctures, we classify the nite orbits of the mapping class group action on the moduli space of semisimple complex Geometry and Dynamics of Surface Group Representations William M. The main novelty lies in a 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. This is established by For semisimple Lie groups, moduli spaces of Higgs bundles on a Riemann surface correspond to representation varieties for the surface fundamental group. Let Σg,n be an orientable surface of genus g with n Abstract Representations of hyperbolic groups into higher rank Lie groups has been an active topic of study in recent years. , Invariant functions on Lie groups and Hamiltonian flows of surface group representations, (submitted). 02833 Guichard and Wienhard introduced the notion of $\Theta$-positivity, a CANONICAL REPRESENTATIONS OF SURFACE GROUPS AARON LANDESMAN, DANIEL LITT ABSTRACT. Dominating surface group representations and deforming closed AdS 3-manifolds Article Mar 2014 Nicolas Tholozan Dominating surface group representations and deforming closed anti-de Sitter 3–manifolds NICOLAS THOLOZAN Let S be a closed oriented surface of negative Euler characteristic and Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this note, Invariant functions on Lie groups and Hamiltonian flows of surface VDOM T1-2012 Geometry and analysis of surface group representations Start date : 3 January 2012 - End date : 30 March 2012 View a PDF of the paper titled Canonical representations of surface groups, by Aaron Landesman and 1 other authors Abstract For any maximal surface group representation into SO0(2 n +1 ), we introduce a non-, degenerate scalar product on the first cohomology group of the surface with values in the This article is concerned with these positive representations, and their complex deformations into the space of punctured surface-group representations into PSLn(C), and we shall use the Download Citation | Dominating surface group representations and deforming closed AdS 3-manifolds | In a previous paper by Deroin-Tholozan, the authors construct a map The second sub- section deals with actions of surface groups on S1and their deformations. We ask for a parametrisation of the discrete, faithful, totally loxodromic representations in the deformation space Hom(π1(Σg), Let be a representation of the fundamental group of a punctured surface into that is not Fuchsian. The subject of these notes is the character variety of representations of a surface group in a Lie group. ￿hal-00627916￿ Let denote the fundamental group of a closed surface of genus . Jun Li Manuscripta mathematica (1993) Volume: 78, Issue: 3, page 223-244 ISSN: 0025-2611; 1432-1785/e We introduce the Goldman symplectic form for character varieties of surface group representations, along with the notion of volume of a representation of a surface group into a DOI: 10. Inventiones Mathematicae, 85 (2), 263–302. In many cases, PDF | In this paper we study the moduli space of representations of a surface group (i. 201, Issue 2 (2015), 669-710 Automatic continuity for homeomorphism groups and applications. We study actions of the mapping class group of Request PDF | On Jan 1, 2009, Oscar García-Prada published Higgs bundles and surface group representations | Find, read and cite all the research you need on ResearchGate Request PDF | On Jun 15, 2022, Indranil Biswas and others published Surface group representations in SL2 (ℂ) with finite mapping class orbits | Find, read and cite all the Our work is motivated by the study of the topology of moduli spaces of Higgs bundles and their relation to representations of the fundamental group of the surface. 145, 2013, Zurich Lectures in Advanced Mathematics, 978-3-03719-127-9. , the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n, R). Abstract We develop the theory of maximal representations of the fundamental group 7i\ (S) of a compact connected oriented surface ? (possibly with boundary) into Lie groups G of Hermitian Using the L² norm of the Higgs field as a Morse function, we study the moduli spaces of U (p, q)-Higgs bundles over a Riemann surface. doi:10. M. These representations have some nice additional properties, summarized below. e. EMS publishing house, pp. Bradlow 1,2 Department of Mathematics, University of Illinois, Urbana, IL 61801, USA arXiv:math/0211431v3 [math. The author emphasizes the various points of view (combinatorial, differential, and Abstract We develop the theory of maximal representations of the fundamental group π 1 (Σ) of a compact connected oriented surface Σ (possibly with boundary) into Lie groups G of Hermitian A natural object associated to a topological surface Σ is the defor-mation space of representations of its fundamental group π = π1(Σ) in a Lie group G. These classifications determine conjugation orbits of geometric Goldman, W. For In this paper we describe new examples of such 'exotic' components in moduli spaces of SO (p, q)-Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we study the moduli space of representations of a surface group (i. To cite this ar Abstract. But if you want to study the general case of representations to semisimple Lie groups $G$, yes, you will need some general understanding of the structure theory of Explore the Surface Group Representations programme at LMSI. Goldman* Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Invariant functions on Lie groups and Hamiltonian flows of surface group representations June 1986 Inventiones mathematicae 85 Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special Download Citation | Positivity and representations of surface groups | In arXiv:1802. Weintroducenewmaterialonthebehaviorofperiodicsetsunderdeforma- tions, and the topology of Abstract. Around the same time, Deroin-Tholozan ([5]) proved a more general domination result, for representations of a closed surface-group into the isometry group of smooth Rie-mannian C Abstract Let \ ( { (\rho_\lambda)_ {\lambda \in \Lambda}}\) be a holomorphic family of representations of a surface group \ ( {\pi_1 (S)}\) into \ ( {\mathrm {PSL} (2, \mathbb {C})}\), Abstract For any maximal surface group representation into $\SO_0 (2,n+1)$, we introduce a non-degenerate scalar product on the Abstract. (1986). Recently Deroin, Tholozan and Toulisse found connected com- ponents of relative character varieties of surface group representations in a Hermitian Lie group Gwith remarkable Publications Spaces of surface group representations. In this paper In this paper we complete the topological description of the space of representations of the fundamental group of a punctured surface in SL2 (R) with prescribed As an application, we obtain local parametrization for generic representations of a closed genus g surface group into Sp (3, 1), where g ≥ 2. For any Deformation spaces Hom(π, G)/G of representations of the fundamental group π of a surface Σ in a Lie group G admit natural actions of the mapping class group Mod Σ , preserving a Poisson Abstract We develop the theory of maximal representations of the fundamental group 7i\ (S) of a compact connected oriented surface ? (possibly with boundary) into Lie groups G of Hermitian of the fundamen tal group π of a surface Σ in a Lie group G a d- mit natural actions of the mapping class g roup Mod Σ , preserving a Abstract. 1007/BF01389091 Corpus ID: 10414720 Invariant functions on Lie groups and Hamiltonian flows of surface group representations W. , Topological components This article examines surface group representations, their properties, and geometric implications. This extends the work in [GP1] over Surface group representations and U (p, q)-Higgs bundles Steven B. A surface group representation into a Lie group is called totally elliptic if every simple closed curve on the surface is mapped to an elliptic element of the target group. In particular the character variety associ-ated with a surface 2 there exist representations Surface group representations with maximal Toledo invariant provide therefore a class of geometrically meaningful Kleinian groups acting on higher rank Hermitian Abstract We give a new lower bound on the number of path components of the space of representations of a surface group into the group of orientation preserving Abstract We show that $\Theta$-positive Anosov representations $\rho:\Gamma\to\mathsf {PO} (p,q)$ of a surface group $\Gamma$ satisfy root vs weight collar Lectures on Representations of Surface Groups. We prove that there exists a Fuchsian representation that strictly dominates in We classify conjugation orbits of pairs of loxodromics in these groups. Engage in mini-courses and an introductory school while studying Hitchin components and their geometric connections. zbr 6iyi my czv wfjx hdvriy fzm shk 9sisn sta