scholarly journals RanknSwapping Algebra for the PSL(n, ℝ) Hitchin Component

2016 ◽  
Vol 2017 (2) ◽  
pp. 583-613 ◽  
Author(s):  
Zhe Sun
Keyword(s):  
Hitchin Component

scholarly journals Convex foliated projective structures and the Hitchin component for ${\rm PSL}_4(\mathbf{R})$

2008 ◽  
Vol 144 (3) ◽  
pp. 381-445 ◽  
Author(s):  
Olivier Guichard ◽  
Anna Wienhard
Keyword(s):  
Projective Structures ◽  
Hitchin Component

On a volume element of a Hitchin component

2012 ◽  
Vol 217 (3) ◽  
pp. 249-264 ◽  
Author(s):  
Yaşar Sözen
Keyword(s):  
Volume Element ◽  
Hitchin Component

SL(∞,ℝ), Higgs Bundles and Quantization

2018 ◽  
pp. 419-432
Author(s):  
Olivier Biquard
Keyword(s):  
Surface Groups ◽  
Higgs Bundles ◽  
Hitchin Component

Nigel Hitchin recently proposed a theory of SL(∞, R)-Higgs bundles which should parametrize a Hitchin component of representations of surface groups into SL(∞, R). This chapter discusses some properties and propose a formal approximation of SL(∞, R) representations by SL(n, R) representations in the large N limit, where n goes to infinity.

scholarly journals REPRESENTATIONS OF SURFACE GROUPS IN THE PROJECTIVE GENERAL LINEAR GROUP

2011 ◽  
Vol 22 (02) ◽  
pp. 223-279 ◽  
Author(s):  
ANDRÉ GAMA OLIVEIRA
Keyword(s):  
Moduli Space ◽  
Riemann Surfaces ◽  
Connected Components ◽  
Higgs Bundles ◽  
Semisimple Lie Group ◽  
Projective Bundles ◽  
Compact Riemann Surfaces ◽  
Hitchin Component ◽  
Projective General Linear Group ◽  
Closed Oriented Surface

Given a closed, oriented surface X of genus g ≥ 2, and a semisimple Lie group G, let [Formula: see text] be the moduli space of reductive representations of π1X in G. We determine the number of connected components of [Formula: see text], for n ≥ 4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in [Formula: see text] is homotopically equivalent to [Formula: see text].

scholarly journals Asymptotics of Higgs bundles in the Hitchin component

2017 ◽  
Vol 307 ◽  
pp. 488-558 ◽  
Author(s):  
Brian Collier ◽  
Qiongling Li
Keyword(s):  
Higgs Bundles ◽  
Hitchin Component

Flows on the $$\mathbf{PGL(V)}$$-Hitchin Component

2020 ◽  
Vol 30 (2) ◽  
pp. 588-692 ◽  
Author(s):  
Zhe Sun ◽  
Anna Wienhard ◽  
Tengren Zhang
Keyword(s):  
Hitchin Component

The dimension of the Hitchin component for triangle groups

2018 ◽  
Vol 200 (1) ◽  
pp. 363-370 ◽  
Author(s):  
D. D. Long ◽  
M. B. Thistlethwaite
Keyword(s):  
Triangle Groups ◽  
Hitchin Component
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