Weyl chamber length compactification of the PSL(2,R) x PSL(2,R) maximal character variety
We study the vectorial length compactification of the space of conjugacy classes of maximal representations of the fundamental group ΓΓ\Gamma of a closed hyperbolic surface ΣΣ\Sigma in PSL(2,R)nPSL(2,R)n\textrm{PSL}(2,{\mathbb{R}})^n. We identify the boundary with the sphere P((ML)n)P((ML)n){\mathbb...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2025
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| In: |
The Glasgow mathematical journal
Year: 2025, Volume: 67, Issue: 1, Pages: 11-33 |
| ISSN: | 1469-509X |
| DOI: | 10.1017/S0017089524000156 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1017/S0017089524000156 Verlag, lizenzpflichtig, Volltext: https://www.cambridge.org/core/journals/glasgow-mathematical-journal/article/weyl-chamber-length-compactification-of-the-textrmpsl2mathbbrtimes-textrmpsl2mathbbr-maximal-character-variety/3FD3EBF841C861C9CA4E617440DA1EB3# 
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| Author Notes: | Marc Burger, Alessandra Iozzi, Anne Parreau and Maria Beatrice Pozzetti |
| Summary: | We study the vectorial length compactification of the space of conjugacy classes of maximal representations of the fundamental group ΓΓ\Gamma of a closed hyperbolic surface ΣΣ\Sigma in PSL(2,R)nPSL(2,R)n\textrm{PSL}(2,{\mathbb{R}})^n. We identify the boundary with the sphere P((ML)n)P((ML)n){\mathbb{P}}(({\mathcal{ML}})^n), where MLML\mathcal{ML} is the space of measured geodesic laminations on ΣΣ\Sigma. In the case n=2n=2n=2, we give a geometric interpretation of the boundary as the space of homothety classes of R2R2{\mathbb{R}}^2-mixed structures on ΣΣ\Sigma. We associate to such a structure a dual tree-graded space endowed with an R2+R2+{\mathbb{R}}_+^2-valued metric, which we show to be universal with respect to actions on products of two RR\mathbb{R}-trees with the given length spectrum. |
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| Item Description: | Online veröffentlicht: 27. September 2024 Gesehen am 26.03.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1469-509X |
| DOI: | 10.1017/S0017089524000156 |