Hitchin's equations on a nonorientable manifold

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Hitchin's equations on a nonorientable manifold. / Ho, Nankuo; Wilkin, Graeme Peter Desmond; Wu, Siye.

In: Communications in Analysis and Geometry, Vol. 26, No. 4, 06.09.2018, p. 857-886.

Research output: Contribution to journalArticle

Harvard

Ho, N, Wilkin, GPD & Wu, S 2018, 'Hitchin's equations on a nonorientable manifold', Communications in Analysis and Geometry, vol. 26, no. 4, pp. 857-886. https://doi.org/10.4310/CAG.2018.v26.n4.a6

APA

Ho, N., Wilkin, G. P. D., & Wu, S. (2018). Hitchin's equations on a nonorientable manifold. Communications in Analysis and Geometry, 26(4), 857-886. https://doi.org/10.4310/CAG.2018.v26.n4.a6

Vancouver

Ho N, Wilkin GPD, Wu S. Hitchin's equations on a nonorientable manifold. Communications in Analysis and Geometry. 2018 Sep 6;26(4):857-886. https://doi.org/10.4310/CAG.2018.v26.n4.a6

Author

Ho, Nankuo ; Wilkin, Graeme Peter Desmond ; Wu, Siye. / Hitchin's equations on a nonorientable manifold. In: Communications in Analysis and Geometry. 2018 ; Vol. 26, No. 4. pp. 857-886.

Bibtex - Download

@article{8d9e8412e2e34d72b36f56cc23d7ffce,
title = "Hitchin's equations on a nonorientable manifold",
abstract = "We define Hitchin{\textquoteright}s moduli space for a principal bundle P, whose structure group is a compact semisimple Lie group K, over a compact non-orientable Riemannian manifold M. We use the Donaldson–Corlette correspondence, which identifies Hitchin{\textquoteright}s moduli space with the moduli space of flat connections, which remains valid when M is non-orientable. This enables us to study Hitchin{\textquoteright}s moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover M~ of M is a K{\"a}hler manifold with odd complex dimension and if the K{\"a}hler form is odd under the non-trivial deck transformation τ on M~, Hitchin{\textquoteright}s moduli space of the pull-back bundle has a hyper-K{\"a}hler structure and admits an involution induced by τ. The fixed-point set is symplectic or Lagrangian with respect to various symplectic structures on the moduli space. We compare the gauge theoretical constructions with the algebraic approach using representation varieties.",
author = "Nankuo Ho and Wilkin, {Graeme Peter Desmond} and Siye Wu",
note = "This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details.",
year = "2018",
month = sep,
day = "6",
doi = "10.4310/CAG.2018.v26.n4.a6",
language = "English",
volume = "26",
pages = "857--886",
journal = "Communications in Analysis and Geometry",
issn = "1019-8385",
publisher = "International Press of Boston, Inc.",
number = "4",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Hitchin's equations on a nonorientable manifold

AU - Ho, Nankuo

AU - Wilkin, Graeme Peter Desmond

AU - Wu, Siye

N1 - 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 - 2018/9/6

Y1 - 2018/9/6

N2 - We define Hitchin’s moduli space for a principal bundle P, whose structure group is a compact semisimple Lie group K, over a compact non-orientable Riemannian manifold M. We use the Donaldson–Corlette correspondence, which identifies Hitchin’s moduli space with the moduli space of flat connections, which remains valid when M is non-orientable. This enables us to study Hitchin’s moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover M~ of M is a Kähler manifold with odd complex dimension and if the Kähler form is odd under the non-trivial deck transformation τ on M~, Hitchin’s moduli space of the pull-back bundle has a hyper-Kähler structure and admits an involution induced by τ. The fixed-point set is symplectic or Lagrangian with respect to various symplectic structures on the moduli space. We compare the gauge theoretical constructions with the algebraic approach using representation varieties.

AB - We define Hitchin’s moduli space for a principal bundle P, whose structure group is a compact semisimple Lie group K, over a compact non-orientable Riemannian manifold M. We use the Donaldson–Corlette correspondence, which identifies Hitchin’s moduli space with the moduli space of flat connections, which remains valid when M is non-orientable. This enables us to study Hitchin’s moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover M~ of M is a Kähler manifold with odd complex dimension and if the Kähler form is odd under the non-trivial deck transformation τ on M~, Hitchin’s moduli space of the pull-back bundle has a hyper-Kähler structure and admits an involution induced by τ. The fixed-point set is symplectic or Lagrangian with respect to various symplectic structures on the moduli space. We compare the gauge theoretical constructions with the algebraic approach using representation varieties.

U2 - 10.4310/CAG.2018.v26.n4.a6

DO - 10.4310/CAG.2018.v26.n4.a6

M3 - Article

VL - 26

SP - 857

EP - 886

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

SN - 1019-8385

IS - 4

ER -