Geometrisation of purely hyperbolic representations in PSL2R

Gianluca Faraco

doi:10.1515/advgeom-2020-0025

Published by De Gruyter January 22, 2021

Geometrisation of purely hyperbolic representations in PSL2R

Gianluca Faraco

From the journal Advances in Geometry

https://doi.org/10.1515/advgeom-2020-0025

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Abstract

Let S be a surface of genus g at least 2. A representation ρ:π1S→PSL2R is said to be purely hyperbolic if its image consists only of hyperbolic elements along with the identity. We may wonder under which conditions such representations arise as the holonomy of a branched hyperbolic structure on S. In this work we characterise them completely, giving necessary and sufficient conditions.

Keywords: Surface; branched hyperbolic structure; holonomy

MSC 2010: 57M50

Acknowledgements

I would like to thank my advisor Stefano Francaviglia for introducing me to this theory and for his constant encouragement. His advice and suggestions have been highly valuable. I also would like to thank Lorenzo Ruffoni for useful comments and suggestions about this work. Finally, I would like to thank the anonymous referee(s) for many useful comments and suggestions.

Communicated by: J. Ratcliffe

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Received: 2018-10-02

Revised: 2019-02-27

Published Online: 2021-01-22

Published in Print: 2021-01-27

Geometrisation of purely hyperbolic representations in PSL2R

Abstract

Acknowledgements

References

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