Positive crossratios, barycenters, trees and applications to maximal representations
We study metric properties of maximal framed representations of fundamental groups of surfaces in symplectic groups over real closed fields, interpreted as actions on Bruhat–Tits buildings endowed with adapted Finsler norms. We prove that the translation length can be computed as intersection with a...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
1 February 2024
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| In: |
Groups, geometry, and dynamics
Year: 2024, Volume: 18, Issue: 3, Pages: 799-847 |
| ISSN: | 1661-7215 |
| DOI: | 10.4171/ggd/767 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.4171/ggd/767 Verlag, kostenfrei, Volltext: https://ems.press/journals/ggd/articles/14199191 
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| Author Notes: | Marc Burger, Alessandra Iozzi, Anne Parreau, and Maria Beatrice Pozzetti |
| Summary: | We study metric properties of maximal framed representations of fundamental groups of surfaces in symplectic groups over real closed fields, interpreted as actions on Bruhat–Tits buildings endowed with adapted Finsler norms. We prove that the translation length can be computed as intersection with a geodesic current, give sufficient conditions guaranteeing that such a current is a multicurve, and, if the current is a measured lamination, construct an isometric embedding of the associated tree in the building. These results are obtained as application of more general results of independent interest on positive crossratios and actions with compatible barycenters. |
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| Item Description: | Gesehen am 20.12.2024 |
| Physical Description: | Online Resource |
| ISSN: | 1661-7215 |
| DOI: | 10.4171/ggd/767 |