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Projective Structures on a Hyperbolic 3-orbifold

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Abstract

We compute and analyse the moduli space of those real projective structures on a hyperbolic 3-orbifold that are modelled on a single ideal tetrahedron in projective space. Parameterisations are given in terms of classical invariants, traces, and geometric invariants, cross-ratios.

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References

  1. Ballas, S. A., Casella, A.: Gluing equations for real projective structures on 3-manifolds. arXiv:1912.12508 (2019)

  2. Ballas, S. A., Danciger, J., Lee, G. -S.: Convex projective structures on nonhyperbolic three-manifolds. Geom. Topol. 22(3), 1593–1646 (2018)

    Article  MathSciNet  Google Scholar 

  3. Benoist, Y.: Convexes divisibles. III. Ann. Sci. École Norm. Sup. (4) 38(5), 793–832 (2005)

    Article  MathSciNet  Google Scholar 

  4. Choi, S.: The Convex Real Projective Orbifolds with Radial or Totally Geodesic Ends: a Survey of Some Partial Results. In: In the Tradition of Ahlfors-Bers. VII, vol. 696. Contemp. Math., pp 51–85. Am. Math. Soc., Providence (2017)

  5. Cooper, D., Long, D., Tillmann, S.: Deforming convex projective manifolds. Geom. Topol. 22(3), 1349–1404 (2018)

    Article  MathSciNet  Google Scholar 

  6. Cooper, D., Long, D. D., Stephan Tillmann, S.: On convex projective manifolds and cusps. Adv. Math. 277, 181–251 (2015)

    Article  MathSciNet  Google Scholar 

  7. Cooper, D., Tillmann, S.: The space of properly-convex structures. arXiv:2009.06568 (2020)

  8. Dunbar, W. D.: Nonfibering spherical 3-orbifolds. Trans. Am. Math. Soc. 341(1), 121–142 (1994)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

We thank the anonymous referee for suggestions that improved the paper. The authors would like to thank the staff at CIRM for an excellent collaboration environment.

Funding

This research was supported through the programme “Research in Pairs” (No. 1811) by the Centre International de Rencontres Mathématiques Luminy in 2017. Research of the first author is supported by FEDER-MEC (grant number PGC2018-095998-B-I00). Research of the second author is supported by an Australian Research Council Future Fellowship (project number FT170100316).

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona and CRM, 08193, Bellaterra, Spain

    Joan Porti

  2. School of Mathematics and Statistics, The University of Sydney, NSW, 2006, Australia

    Stephan Tillmann

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  1. Joan Porti
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  2. Stephan Tillmann
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Correspondence to Joan Porti.

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Porti, J., Tillmann, S. Projective Structures on a Hyperbolic 3-orbifold. Acta Math Vietnam 46, 347–355 (2021). https://doi.org/10.1007/s40306-021-00419-0

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  • DOI: https://doi.org/10.1007/s40306-021-00419-0

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