Higgs bundles over cell complexes and representations of finitely generated 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 notion 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 $SL(r, \mathbb{C})$ character variety of a finitely presented group $\Gamma$ is homeomorphic to the moduli space of rank $r$ Higgs bundles over an admissible complex $X$ with $\pi_1(X) = \Gamma$. A key role is played by the theory of harmonic maps defined on singular domains.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2016
- DOI:
- 10.48550/arXiv.1605.04625
- arXiv:
- arXiv:1605.04625
- Bibcode:
- 2016arXiv160504625D
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 20 pages