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Geometry of compact
complex manifolds associated to generalized quasi-Fuchsian
representations
David Dumas and Andrew Sanders |
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Geometry & Topology 24 (2020) 1615–1693
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Abstract |
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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 . |
Keywords
Anosov representations, complex manifolds, flag varieties
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Mathematical Subject Classification 2010
Primary: 32Q30, 57M50
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References |
Publication
Received: 9 June 2017
Revised: 25 June 2019
Accepted: 14 October 2019
Published: 10 November 2020
Proposed: Anna Wienhard
Seconded: Jean-Pierre Otal, Benson Farb
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Authors |
| David Dumas | |
| Department of Mathematics,
Statistics, and Computer Science University of Illinois at Chicago Chicago, IL United States |
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| Andrew Sanders | |
| Mathematisches Institut Universität Heidelberg Heidelberg Germany |
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