2020 Geometry of compact complex manifolds associated to generalized quasi-Fuchsian representations
David Dumas, Andrew Sanders
Geom. Topol. 24(4): 1615-1693 (2020). DOI: 10.2140/gt.2020.24.1615

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 G. We compute the homology of the manifolds obtained from G–Fuchsian representations and their Anosov deformations, where G 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 PSL3–Fuchsian representations are topological fiber bundles over a surface, and we conjecture this holds for all simple G.

Citation

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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

Information

Received: 9 June 2017; Revised: 25 June 2019; Accepted: 14 October 2019; Published: 2020
First available in Project Euclid: 17 November 2020

zbMATH: 07274786
MathSciNet: MR4173918
Digital Object Identifier: 10.2140/gt.2020.24.1615

Subjects:
Primary: 32Q30 , 57M50

Keywords: Anosov representations , Complex Manifolds , flag varieties

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.24 • No. 4 • 2020
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