Rank one Higgs bundles and representations of fundamental groups of Riemann surfaces

DOI10.1090/memo/0904zbMath1158.14001arXivmath/0402429OpenAlexW2023099939MaRDI QIDQ5385843

Eugene Z. Xia, William M. Goldman

Publication date: 7 May 2008

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402429

zbMATH Keywords

fundamental groupmoduli spaceRiemann surfacegroupoidtwistor spaceHiggs bundleHodge structurehyperkahler structure

Mathematics Subject Classification ID

Moduli problems for differential geometric structures (58D27) Moduli problems for topological structures (58D29) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Research exposition (monographs, survey articles) pertaining to functions of a complex variable (30-02) Fundamental group, presentations, free differential calculus (57M05) Vector bundles on curves and their moduli (14H60) Riemann surfaces (30Fxx)

Related Items (12)

On the geometric P=W conjecture ⋮ Introduction to Nonabelian Hodge Theory ⋮ Recent results and conjectures on the non abelian Hodge theory of curves ⋮ Eisenstein metrics ⋮ On the automorphisms of a rank one Deligne-Hitchin moduli space ⋮ Deformations of twisted harmonic maps and variation of the energy ⋮ Moduli spaces of Higgs bundles - old and new ⋮ Goldman flows on the Jacobian ⋮ Nonabelian Hodge theory and vector valued modular forms ⋮ Deligne pairings and families of rank one local systems on algebraic curves ⋮ Hyperbolic band theory through Higgs bundles ⋮ Twisted translation flows and effective weak mixing

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