Higgs bundles over cell complexes and representations of finitely presented groups

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Higgs bundles over cell complexes and representations of finitely presented groups. / Daskalopoulos, Georgios; Mese, Chikako; Wilkin, Graeme Peter Desmond.

In: Pacific Journal of Mathematics, Vol. 296, No. 1, 01.05.2018, p. 31-55.

Research output: Contribution to journalArticle

Harvard

Daskalopoulos, G, Mese, C & Wilkin, GPD 2018, 'Higgs bundles over cell complexes and representations of finitely presented groups', Pacific Journal of Mathematics, vol. 296, no. 1, pp. 31-55. https://doi.org/10.2140/pjm.2018.296.31

APA

Daskalopoulos, G., Mese, C., & Wilkin, G. P. D. (2018). Higgs bundles over cell complexes and representations of finitely presented groups. Pacific Journal of Mathematics, 296(1), 31-55. https://doi.org/10.2140/pjm.2018.296.31

Vancouver

Daskalopoulos G, Mese C, Wilkin GPD. Higgs bundles over cell complexes and representations of finitely presented groups. Pacific Journal of Mathematics. 2018 May 1;296(1):31-55. https://doi.org/10.2140/pjm.2018.296.31

Author

Daskalopoulos, Georgios ; Mese, Chikako ; Wilkin, Graeme Peter Desmond. / Higgs bundles over cell complexes and representations of finitely presented groups. In: Pacific Journal of Mathematics. 2018 ; Vol. 296, No. 1. pp. 31-55.

Bibtex - Download

@article{c1aa6a75051549fcaa7c8be94536b272,
title = "Higgs bundles over cell complexes and representations of finitely presented groups",
abstract = "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.",
author = "Georgios Daskalopoulos and Chikako Mese and Wilkin, {Graeme Peter Desmond}",
note = "{\circledC} 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.",
year = "2018",
month = "5",
day = "1",
doi = "10.2140/pjm.2018.296.31",
language = "English",
volume = "296",
pages = "31--55",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "1",

}

RIS (suitable for import to EndNote) - Download

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 -