2021/10/28 by Daniele Alessandrini, Alessandrini, Daniele, Colin Davalo +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.DG #math.GT
paper · pdf · doi:10.48550/arxiv.2110.15407
46 pages, comments are welcome!
arxiv created 2021/10/28 · openalex publication_date 2021/10/28 · arxiv updated 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.