The Dimension of the Hitchin Component for Triangle Groups
نویسندگان
چکیده
Representation varieties of closed surface groups into SL(n,R) have been studied extensively by Hitchin and Labourie, and the dimension of a certain distinguished component of the variety was obtained by Hitchin using Higgs bundles. Here we determine the corresponding dimension for representations of triangle groups into SL(n,R), generalising some earlier work of Choi and Goldman in the case n = 3.
منابع مشابه
On the Automorphisms of a Rank One Deligne–Hitchin Moduli Space
Let X be a compact connected Riemann surface of genus g ≥ 2, and let MDH be the rank one Deligne–Hitchin moduli space associated to X. It is known thatMDH is the twistor space for the hyper-Kähler structure on the moduli space of rank one holomorphic connections on X. We investigate the group Aut(MDH) of all holomorphic automorphisms of MDH. The connected component of Aut(MDH) containing the id...
متن کاملOn the boundary behavior of left-invariant Hitchin and hypo flows
We investigate left-invariant Hitchin and hypo flows on 5-, 6and 7-dimensional Lie groups. They provide Riemannian cohomogeneity-one manifolds of one dimension higher with holonomy contained in SU(3), G2 and Spin(7), respectively, which are in general geodesically incomplete. Generalizing results of Conti, we prove that for large classes of solvable Lie groups G these manifolds cannot be comple...
متن کاملFeature Dimension Reduction of Multisensor Data Fusion using Principal Component Fuzzy Analysis
These days, the most important areas of research in many different applications, with different tools, are focused on how to get awareness. One of the serious applications is the awareness of the behavior and activities of patients. The importance is due to the need of ubiquitous medical care for individuals. That the doctor knows the patient's physical condition, sometimes is very important. O...
متن کاملSimple Root Flows for Hitchin Representations
Anosov representations ([19, 15]) from a hyperbolic group to a semi-simple Lie group are characterized by their dynamical nature. In the context of projective Anosov representations, we [7] previously associated a metric Anosov flow to such a representation and showed that the (thermo)dynamical properties of this flow yield in turn new structures on the deformation space of these representation...
متن کاملIdentifying the Factors Affecting the Empowerment of Rural Tourism Destinations (Case: Lorestan Province)
In recent decades, rural tourism as a complementary activity of agriculture and animal husbandry has always been a factor in improving the economic conditions of rural residents. Based on this research was conducted to identify factors affecting the empowerment of rural tourism destinations. Data collection was done by using two methods of archiving and scrolling through interviews and question...
متن کامل