Projective Structures with (Quasi-)Hitchin Holonomy

Daniele Alessandrini; Colin Davalo; Qiongling Li

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arXiv · 2110.15407

Projective Structures with (Quasi-)Hitchin Holonomy

Daniele Alessandrini·Colin Davalo·Qiongling Li

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Abstract

In this paper we investigate the properties of the real and complex projective structures associated to Hitchin and quasi-Hitchin representations that were originally constructed using Guichard-Wienhard's theory of domains of discontinuity. We determine the topology of the underlying manifolds and we prove that some of these geometric structures are fibered in a special standard way. In order to prove these results, we give two new ways to construct these geometric structures: we construct them using gauge theory, flat bundles and Higgs bundles, and we also give a new geometric way to construct them.

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BibTeX RIS

Daniele Alessandrini, Colin Davalo, Qiongling Li. 2021-10-28. Projective Structures with (Quasi-)Hitchin Holonomy. https://arxiv.org/abs/2110.15407

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