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) Chapter/Article |
| Language: | English |
| Published: |
31 Mar 2021
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| In: |
Arxiv
Year: 2021, Pages: 1-56 |
| DOI: | 10.48550/arXiv.2103.17161 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.2103.17161 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2103.17161 
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| Author Notes: | M. Burger, A. Iozzi, A. Parreau, and M.B. 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: | Identifizierung der Ressource nach: Last revised 22 Sep 2021 Gesehen am 29.09.2022 |
| Physical Description: | Online Resource |
| DOI: | 10.48550/arXiv.2103.17161 |