scholarly journals Surface Group Representations and U(p, q)-Higgs Bundles

2003 ◽  
Vol 64 (1) ◽  
pp. 111-170 ◽  
Author(s):  
Steven B. Bradlow ◽  
Oscar García-Prada ◽  
Peter B. Gothen
Keyword(s):  
Surface Group ◽  
Higgs Bundles ◽  
Group Representations ◽  
Surface Group Representations

scholarly journals Surface group representations with maximal Toledo invariant

2010 ◽  
Vol 172 (1) ◽  
pp. 517-566 ◽  
Author(s):  
Marc Burger ◽  
Alessandra Iozzi ◽  
Anna Wienhard
Keyword(s):  
Surface Group ◽  
Group Representations ◽  
Toledo Invariant ◽  
Surface Group Representations

Various Generalizations and Deformations of PSL(2,ℝ) Surface Group Representations and their Higgs Bundles

2018 ◽  
pp. 471-502
Author(s):  
Brian Collier
Keyword(s):  
Fundamental Group ◽  
Vector Bundles ◽  
Surface Group ◽  
Closed Surface ◽  
Connected Components ◽  
Character Variety ◽  
Higgs Bundles ◽  
Group Representations ◽  
Symmetric Powers ◽  
Higher Rank

The goal of this chapter is to examine the various ways in which Fuchsian representations of the fundamental group of a closed surface of genus g into PSL(2, R) and their associated Higgs bundles generalize to the higher-rank groups PSL(n, R), PSp(2n, R), SO0(2, n), SO0(n,n+1) and PU(n, n). For the SO0(n,n+1)-character variety, it parameterises n(2g−2) new connected components as the total spaces of vector bundles over appropriate symmetric powers of the surface, and shows how these components deform in the character variety. This generalizes results of Hitchin for PSL(2, R).

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