Abstract
We study the topology and geometry of compact complex manifolds associated to Anosov representations of surface groups and other hyperbolic groups in a complex semisimple Lie group . We compute the homology of the manifolds obtained from –Fuchsian representations and their Anosov deformations, where is simple. We show that in sufficiently high rank, these quotient complex manifolds are not Kähler. We also obtain results about their Picard groups and existence of meromorphic functions.
In a final section, we apply our topological results to some explicit families of domains and derive closed formulas for certain topological invariants. We also show that the manifolds associated to Anosov deformations of –Fuchsian representations are topological fiber bundles over a surface, and we conjecture this holds for all simple .
Citation
David Dumas. Andrew Sanders. "Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations." Geom. Topol. 24 (4) 1615 - 1693, 2020. https://doi.org/10.2140/gt.2020.24.1615
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