Higgs bundles over cell complexes and representations of finitely presented groups

TY - JOUR

T1 - Higgs bundles over cell complexes and representations of finitely presented groups

AU - Daskalopoulos, Georgios

AU - Mese, Chikako

AU - Wilkin, Graeme Peter Desmond

N1 - © 2018 Mathematical Sciences Publishers. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - The purpose of this paper is to extend the Donaldson–Corlette theorem to the case of vector bundles over cell complexes. We define the notions of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham and Higgs moduli spaces. The main theorem is that the SL(r,C) character variety of a finitely presented group Γ is homeomorphic to the moduli space of rank-r Higgs bundles over an admissible complex X with π1(X)=Γ. A key role is played by the theory of harmonic maps defined on singular domains.

AB - The purpose of this paper is to extend the Donaldson–Corlette theorem to the case of vector bundles over cell complexes. We define the notions of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham and Higgs moduli spaces. The main theorem is that the SL(r,C) character variety of a finitely presented group Γ is homeomorphic to the moduli space of rank-r Higgs bundles over an admissible complex X with π1(X)=Γ. A key role is played by the theory of harmonic maps defined on singular domains.

U2 - 10.2140/pjm.2018.296.31

DO - 10.2140/pjm.2018.296.31

M3 - Article

VL - 296

SP - 31

EP - 55

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -