WebIntroduction What is a Higgs bundle? I X { closed Riemann surface of genus g; I K X = T1;0X { the holomorphic cotangent bundle of X. De nition A Higgs bundle on X is a pair (E;˚), where I E !X is holomorphic vector bundle; I ˚is a holomorphic 1-form with values in End(E), i.e., ˚2H0(X;End(E) K X). Discrete invariants: d = deg(E); n = rk(E): Example WebTEICHMULLER SPACES ¨ STEVEN BRADLOW ... Moduli spaces of Higgs bundles 38 6.1. Stability conditions and moduli spaces 38 6.2. Local structure of the moduli spaces 39 6.3. The Hitchin map 40 6.4. The Hitchin–Kobayashi correspondence 41 7. The generalized Cayley correspondence 42
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WebHiggs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying … WebThe notion of a Higgs bundle was introduced by Hitchin in [14] and has been widely studied from di erent points of view. The moduli space of Higgs bundles includes Teichmuller space when we consider discrete and faithful representations to SL(2;R) (see [10], [32]) and further generalizes to the concept of higher Teichmuller orcheal
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WebTeichmuller spaces. They are now called Hitchin components or higher Teichmuller spaces. The rst works which related geometric structures and higher Teichmuller theory are Choi{Goldman [11] and Guichard{Wienhard [23], showing how the low-rank Hitchin components can be used as parameter spaces of special geometric structures on closed … Webfolds. In Chapter 7 we geometrically quantize the Higgs line bundle moduli space, and investigate the di culties of generalising the techniques used to the higher rank spaces. In particular we construct a projectively at Hitchin connection on the bundle of quantum spaces over Teichmuller space. As far as the author is aware, this is an original ... Webof the orbifold fundamental group. Moreover, the Teichmuller space in the orbifold case was studied in [38], as well as the topology of the moduli space of Higgs bundles in the orbifold situation for rank 2 bundles. Under the correspondence between parabolic Higgs bundles and Higgs V-bundles, we map orche slides