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 -